# How do you solve x^2 – 3x = 7x – 2?

Aug 5, 2015

$x = 5 \pm \sqrt{23}$

#### Explanation:

${x}^{2} - 3 x = 7 x - 2$

is equivalent (subtract $\left(7 x - 2\right)$ from both sides) to
${x}^{2} - 10 x + 2 = 0$

Using the quadratic formula for roots
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
which in this case gives
$\textcolor{w h i t e}{\text{XXXX}}$x= (10+-sqrt(10^2-4(1)(2)))/(2(1)

$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$= 5+-sqrt(23