# How do you solve x^2-4x=6?

May 24, 2015

First, subtract 6 from both sides:

${x}^{2} - 4 x - 6 = 0$

No combination of two factors of -6 will add up to -4, so you'll have to use the quadratic formula to solve this.

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

$x = \frac{- \left(- 4\right) \pm \sqrt{{\left(- 4\right)}^{2} - 4 \left(1\right) \left(- 6\right)}}{2 \left(1\right)}$

$x = \frac{4 \pm \sqrt{16 - \left(- 24\right)}}{2}$

$x = 2 \pm \sqrt{4 - \left(- 6\right)}$

$x = 2 \pm \sqrt{10}$