Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $30x$, the least common multiple of $30,10,x$.
$$x\times 50=3x\times 4\times \frac{200}{x}$$
Multiply $3$ and $4$ to get $12$.
$$x\times 50=12x\times \frac{200}{x}$$
Express $12\times \frac{200}{x}$ as a single fraction.
$$x\times 50=\frac{12\times 200}{x}x$$
Multiply $12$ and $200$ to get $2400$.
$$x\times 50=\frac{2400}{x}x$$
Express $\frac{2400}{x}x$ as a single fraction.
$$x\times 50=\frac{2400x}{x}$$
Subtract $\frac{2400x}{x}$ from both sides.
$$x\times 50-\frac{2400x}{x}=0$$
To add or subtract expressions, expand them to make their denominators the same. Multiply $x\times 50$ times $\frac{x}{x}$.
$$\frac{x\times 50x}{x}-\frac{2400x}{x}=0$$
Since $\frac{x\times 50x}{x}$ and $\frac{2400x}{x}$ have the same denominator, subtract them by subtracting their numerators.
$$\frac{x\times 50x-2400x}{x}=0$$
Do the multiplications in $x\times 50x-2400x$.
$$\frac{50x^{2}-2400x}{x}=0$$
Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x$.
$$50x^{2}-2400x=0$$
Factor out $x$.
$$x\left(50x-2400\right)=0$$
To find equation solutions, solve $x=0$ and $50x-2400=0$.
$$x=0$$ $$x=48$$
Variable $x$ cannot be equal to $0$.
$$x=48$$
Steps Using the Quadratic Formula
Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $30x$, the least common multiple of $30,10,x$.
$$x\times 50=3x\times 4\times \frac{200}{x}$$
Multiply $3$ and $4$ to get $12$.
$$x\times 50=12x\times \frac{200}{x}$$
Express $12\times \frac{200}{x}$ as a single fraction.
$$x\times 50=\frac{12\times 200}{x}x$$
Multiply $12$ and $200$ to get $2400$.
$$x\times 50=\frac{2400}{x}x$$
Express $\frac{2400}{x}x$ as a single fraction.
$$x\times 50=\frac{2400x}{x}$$
Subtract $\frac{2400x}{x}$ from both sides.
$$x\times 50-\frac{2400x}{x}=0$$
To add or subtract expressions, expand them to make their denominators the same. Multiply $x\times 50$ times $\frac{x}{x}$.
$$\frac{x\times 50x}{x}-\frac{2400x}{x}=0$$
Since $\frac{x\times 50x}{x}$ and $\frac{2400x}{x}$ have the same denominator, subtract them by subtracting their numerators.
$$\frac{x\times 50x-2400x}{x}=0$$
Do the multiplications in $x\times 50x-2400x$.
$$\frac{50x^{2}-2400x}{x}=0$$
Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x$.
$$50x^{2}-2400x=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $50$ for $a$, $-2400$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
Now solve the equation $x=\frac{2400±2400}{100}$ when $±$ is plus. Add $2400$ to $2400$.
$$x=\frac{4800}{100}$$
Divide $4800$ by $100$.
$$x=48$$
Now solve the equation $x=\frac{2400±2400}{100}$ when $±$ is minus. Subtract $2400$ from $2400$.
$$x=\frac{0}{100}$$
Divide $0$ by $100$.
$$x=0$$
The equation is now solved.
$$x=48$$ $$x=0$$
Variable $x$ cannot be equal to $0$.
$$x=48$$
Steps for Completing the Square
Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $30x$, the least common multiple of $30,10,x$.
$$x\times 50=3x\times 4\times \frac{200}{x}$$
Multiply $3$ and $4$ to get $12$.
$$x\times 50=12x\times \frac{200}{x}$$
Express $12\times \frac{200}{x}$ as a single fraction.
$$x\times 50=\frac{12\times 200}{x}x$$
Multiply $12$ and $200$ to get $2400$.
$$x\times 50=\frac{2400}{x}x$$
Express $\frac{2400}{x}x$ as a single fraction.
$$x\times 50=\frac{2400x}{x}$$
Subtract $\frac{2400x}{x}$ from both sides.
$$x\times 50-\frac{2400x}{x}=0$$
To add or subtract expressions, expand them to make their denominators the same. Multiply $x\times 50$ times $\frac{x}{x}$.
$$\frac{x\times 50x}{x}-\frac{2400x}{x}=0$$
Since $\frac{x\times 50x}{x}$ and $\frac{2400x}{x}$ have the same denominator, subtract them by subtracting their numerators.
$$\frac{x\times 50x-2400x}{x}=0$$
Do the multiplications in $x\times 50x-2400x$.
$$\frac{50x^{2}-2400x}{x}=0$$
Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x$.
$$50x^{2}-2400x=0$$
Divide both sides by $50$.
$$\frac{50x^{2}-2400x}{50}=\frac{0}{50}$$
Dividing by $50$ undoes the multiplication by $50$.
Divide $-48$, the coefficient of the $x$ term, by $2$ to get $-24$. Then add the square of $-24$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.
