-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)-6=0

We multiply parentheses

-9x^2-45x-6=0

a = -9; b = -45; c = -6;
Δ = b2-4ac
Δ = -452-4·(-9)·(-6)
Δ = 1809
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:

$\sqrt{\Delta}=\sqrt{1809}=\sqrt{9*201}=\sqrt{9}*\sqrt{201}=3\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{201}}{2*-9}=\frac{45-3\sqrt{201}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{201}}{2*-9}=\frac{45+3\sqrt{201}}{-18}
$