Solve 5x((2x)/(3)-(3x)/(5))+1=2x-2(x-1) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$5x( \frac{ 2x }{ 3 } - \frac{ 3x }{ 5 } )+1=2x-2(x-1)$$

Solve for x

$x=\sqrt{3}\approx 1.732050808$
$x=-\sqrt{3}\approx -1.732050808$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply both sides of the equation by $15$, the least common multiple of $3,5$.

$$75x\left(\frac{2x}{3}-\frac{3x}{5}\right)+15=30x-30\left(x-1\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3$ and $5$ is $15$. Multiply $\frac{2x}{3}$ times $\frac{5}{5}$. Multiply $\frac{3x}{5}$ times $\frac{3}{3}$.

$$75x\left(\frac{5\times 2x}{15}-\frac{3\times 3x}{15}\right)+15=30x-30\left(x-1\right)$$

Since $\frac{5\times 2x}{15}$ and $\frac{3\times 3x}{15}$ have the same denominator, subtract them by subtracting their numerators.

$$75x\times \frac{5\times 2x-3\times 3x}{15}+15=30x-30\left(x-1\right)$$

Do the multiplications in $5\times 2x-3\times 3x$.

$$75x\times \frac{10x-9x}{15}+15=30x-30\left(x-1\right)$$

Combine like terms in $10x-9x$.

$$75x\times \frac{x}{15}+15=30x-30\left(x-1\right)$$

Cancel out $15$, the greatest common factor in $75$ and $15$.

$$5xx+15=30x-30\left(x-1\right)$$

Use the distributive property to multiply $-30$ by $x-1$.

$$5xx+15=30x-30x+30$$

Combine $30x$ and $-30x$ to get $0$.

$$5xx+15=30$$

Multiply $x$ and $x$ to get $x^{2}$.

$$5x^{2}+15=30$$

Subtract $15$ from both sides.

$$5x^{2}=30-15$$

Subtract $15$ from $30$ to get $15$.

$$5x^{2}=15$$

Divide both sides by $5$.

$$x^{2}=\frac{15}{5}$$

Divide $15$ by $5$ to get $3$.

$$x^{2}=3$$

Take the square root of both sides of the equation.

$$x=\sqrt{3}$$ $$x=-\sqrt{3}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by $15$, the least common multiple of $3,5$.

$$75x\left(\frac{2x}{3}-\frac{3x}{5}\right)+15=30x-30\left(x-1\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3$ and $5$ is $15$. Multiply $\frac{2x}{3}$ times $\frac{5}{5}$. Multiply $\frac{3x}{5}$ times $\frac{3}{3}$.

$$75x\left(\frac{5\times 2x}{15}-\frac{3\times 3x}{15}\right)+15=30x-30\left(x-1\right)$$

Since $\frac{5\times 2x}{15}$ and $\frac{3\times 3x}{15}$ have the same denominator, subtract them by subtracting their numerators.

$$75x\times \frac{5\times 2x-3\times 3x}{15}+15=30x-30\left(x-1\right)$$

Do the multiplications in $5\times 2x-3\times 3x$.

$$75x\times \frac{10x-9x}{15}+15=30x-30\left(x-1\right)$$

Combine like terms in $10x-9x$.

$$75x\times \frac{x}{15}+15=30x-30\left(x-1\right)$$

Cancel out $15$, the greatest common factor in $75$ and $15$.

$$5xx+15=30x-30\left(x-1\right)$$

Use the distributive property to multiply $-30$ by $x-1$.

$$5xx+15=30x-30x+30$$

Combine $30x$ and $-30x$ to get $0$.

$$5xx+15=30$$

Multiply $x$ and $x$ to get $x^{2}$.

$$5x^{2}+15=30$$

Subtract $30$ from both sides.

$$5x^{2}+15-30=0$$

Subtract $30$ from $15$ to get $-15$.

$$5x^{2}-15=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $5$ for $a$, $0$ for $b$, and $-15$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-15\right)}}{2\times 5}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 5\left(-15\right)}}{2\times 5}$$

Multiply $-4$ times $5$.

$$x=\frac{0±\sqrt{-20\left(-15\right)}}{2\times 5}$$

Multiply $-20$ times $-15$.

$$x=\frac{0±\sqrt{300}}{2\times 5}$$

Take the square root of $300$.

$$x=\frac{0±10\sqrt{3}}{2\times 5}$$

Multiply $2$ times $5$.

$$x=\frac{0±10\sqrt{3}}{10}$$

Now solve the equation $x=\frac{0±10\sqrt{3}}{10}$ when $±$ is plus.

$$x=\sqrt{3}$$

Now solve the equation $x=\frac{0±10\sqrt{3}}{10}$ when $±$ is minus.

$$x=-\sqrt{3}$$

The equation is now solved.

$$x=\sqrt{3}$$ $$x=-\sqrt{3}$$