# How do you solve 3x^2 – 2x = 15x – 10?

Jan 26, 2016

$x = \textcolor{red}{5} , \textcolor{b l u e}{\frac{2}{3}}$

#### Explanation:

Gather all terms on one side.

3x^2-2x-15x+10=0"

Combine like terms.

$3 {x}^{2} - 17 x + 10 = 0$ is a quadratic equation in the form $a {x}^{2} + b x + c$, where $a = 3 , b = - 17 , c = 10$.

Use the quadratic formula to solve the equation.

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Substitute the values from the equation.

$x = \frac{- \left(- 17\right) \pm \sqrt{{\left(- 17\right)}^{2} - 4 \cdot 3 \cdot 10}}{2 \cdot 3}$

Simplify.

$x = \frac{17 \pm \sqrt{289 - 120}}{6}$

Simplify.

$x = \frac{17 \pm \sqrt{169}}{6}$

Simplify.

$x = \frac{17 \pm 13}{6}$

Solve for $x$.

$\textcolor{red}{x = \frac{17 + 13}{6}}$

$\textcolor{red}{x = \frac{30}{6}}$

$\textcolor{red}{x = 5}$

$\textcolor{b l u e}{x = \frac{17 - 13}{6}}$

$\textcolor{b l u e}{x = \frac{4}{6}}$

Reduce the fraction.

$\textcolor{b l u e}{x = \frac{2}{3}}$