Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $42x$, the least common multiple of $6,7x,7$.
$$7x\times 10x+6\times 48x=48x$$
Multiply $7$ and $10$ to get $70$.
$$70xx+6\times 48x=48x$$
Multiply $x$ and $x$ to get $x^{2}$.
$$70x^{2}+6\times 48x=48x$$
Multiply $6$ and $48$ to get $288$.
$$70x^{2}+288x=48x$$
Subtract $48x$ from both sides.
$$70x^{2}+288x-48x=0$$
Combine $288x$ and $-48x$ to get $240x$.
$$70x^{2}+240x=0$$
Factor out $x$.
$$x\left(70x+240\right)=0$$
To find equation solutions, solve $x=0$ and $70x+240=0$.
$$x=0$$ $$x=-\frac{24}{7}$$
Variable $x$ cannot be equal to $0$.
$$x=-\frac{24}{7}$$
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 $42x$, the least common multiple of $6,7x,7$.
$$7x\times 10x+6\times 48x=48x$$
Multiply $7$ and $10$ to get $70$.
$$70xx+6\times 48x=48x$$
Multiply $x$ and $x$ to get $x^{2}$.
$$70x^{2}+6\times 48x=48x$$
Multiply $6$ and $48$ to get $288$.
$$70x^{2}+288x=48x$$
Subtract $48x$ from both sides.
$$70x^{2}+288x-48x=0$$
Combine $288x$ and $-48x$ to get $240x$.
$$70x^{2}+240x=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $70$ for $a$, $240$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{-240±\sqrt{240^{2}}}{2\times 70}$$
Take the square root of $240^{2}$.
$$x=\frac{-240±240}{2\times 70}$$
Multiply $2$ times $70$.
$$x=\frac{-240±240}{140}$$
Now solve the equation $x=\frac{-240±240}{140}$ when $±$ is plus. Add $-240$ to $240$.
$$x=\frac{0}{140}$$
Divide $0$ by $140$.
$$x=0$$
Now solve the equation $x=\frac{-240±240}{140}$ when $±$ is minus. Subtract $240$ from $-240$.
$$x=-\frac{480}{140}$$
Reduce the fraction $\frac{-480}{140}$ to lowest terms by extracting and canceling out $20$.
$$x=-\frac{24}{7}$$
The equation is now solved.
$$x=0$$ $$x=-\frac{24}{7}$$
Variable $x$ cannot be equal to $0$.
$$x=-\frac{24}{7}$$
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 $42x$, the least common multiple of $6,7x,7$.
$$7x\times 10x+6\times 48x=48x$$
Multiply $7$ and $10$ to get $70$.
$$70xx+6\times 48x=48x$$
Multiply $x$ and $x$ to get $x^{2}$.
$$70x^{2}+6\times 48x=48x$$
Multiply $6$ and $48$ to get $288$.
$$70x^{2}+288x=48x$$
Subtract $48x$ from both sides.
$$70x^{2}+288x-48x=0$$
Combine $288x$ and $-48x$ to get $240x$.
$$70x^{2}+240x=0$$
Divide both sides by $70$.
$$\frac{70x^{2}+240x}{70}=\frac{0}{70}$$
Dividing by $70$ undoes the multiplication by $70$.
$$x^{2}+\frac{240}{70}x=\frac{0}{70}$$
Reduce the fraction $\frac{240}{70}$ to lowest terms by extracting and canceling out $10$.
$$x^{2}+\frac{24}{7}x=\frac{0}{70}$$
Divide $0$ by $70$.
$$x^{2}+\frac{24}{7}x=0$$
Divide $\frac{24}{7}$, the coefficient of the $x$ term, by $2$ to get $\frac{12}{7}$. Then add the square of $\frac{12}{7}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.
Factor $x^{2}+\frac{24}{7}x+\frac{144}{49}$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.
