-4x(x+9)=-9x-6

Solution for -4x(x+9)=-9x-6 equation:

-4x(x+9)=-9x-6

We move all terms to the left:

-4x(x+9)-(-9x-6)=0

We multiply parentheses

-4x^2-36x-(-9x-6)=0

We get rid of parentheses

-4x^2-36x+9x+6=0

We add all the numbers together, and all the variables

-4x^2-27x+6=0

a = -4; b = -27; c = +6;
Δ = b2-4ac
Δ = -272-4·(-4)·6
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-5\sqrt{33}}{2*-4}=\frac{27-5\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+5\sqrt{33}}{2*-4}=\frac{27+5\sqrt{33}}{-8}
$