Solve for: -6x^2-12x=-11

Expression: $-6x^{2}-12x=-11$

Add $11$ to both sides

$-6x^{2}-12x+11=-11+11$

Simplify

$-6x^{2}-12x+11=0$

Solve with the quadratic formula

$x_{1,2}=\frac{-(-12)\pm \sqrt{(-12)^{2}-4(-6)\cdot 11}}{2(-6)}$

$\sqrt{(-12)^{2}-4(-6)\cdot 11}=2\sqrt{102}$

$x_{1,2}=\frac{-(-12)\pm 2\sqrt{102}}{2(-6)}$

Separate the solutions

$x_{1}=\frac{-(-12)+2\sqrt{102}}{2(-6)},x_{2}=\frac{-(-12)-2\sqrt{102}}{2(-6)}$

$x=\frac{-(-12)+2\sqrt{102}}{2(-6)}:{\quad}-\frac{6+\sqrt{102}}{6}$

$=-\frac{6+\sqrt{102}}{6}$

$x=\frac{-(-12)-2\sqrt{102}}{2(-6)}:{\quad}\frac{\sqrt{102}-6}{6}$

$=\frac{\sqrt{102}-6}{6}$

The solutions to the quadratic equation are:

$x=-\frac{6+\sqrt{102}}{6},x=\frac{\sqrt{102}-6}{6}$