-9x(x+5)+6=-12

Solution for -9x(x+5)+6=-12 equation:

-9x(x+5)+6=-12

We move all terms to the left:

-9x(x+5)+6-(-12)=0

We add all the numbers together, and all the variables

-9x(x+5)+18=0

We multiply parentheses

-9x^2-45x+18=0

a = -9; b = -45; c = +18;
Δ = b2-4ac
Δ = -452-4·(-9)·18
Δ = 2673
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2673}=\sqrt{81*33}=\sqrt{81}*\sqrt{33}=9\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-9\sqrt{33}}{2*-9}=\frac{45-9\sqrt{33}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+9\sqrt{33}}{2*-9}=\frac{45+9\sqrt{33}}{-18}
$