# How do you solve x^2 - 3x = -6x - 1?

Aug 2, 2015

The solutions for the expression are
color(green)(x=(-3-sqrt5)/2, x=(-3+sqrt5)/2

#### Explanation:

x^2−3x=−6x−1

x^2−3x+6x+1=0

${x}^{2} + 3 x + 1 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = 3 , c = 1$

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$
$= {\left(3\right)}^{2} - \left(4 \cdot \left(1\right) \cdot 1\right)$
$= 9 - 4 = 5$

As $\Delta > 0$ there are two solutions.

The solutions are found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{\left(- 3\right) \pm \sqrt{5}}{2 \cdot 1} = \frac{- 3 \pm \sqrt{5}}{2}$

The solutions for the expression are:
color(green)(x=(-3-sqrt5)/2, x=(-3+sqrt5)/2