2x(-9x+12)=-9

Solution for 2x(-9x+12)=-9 equation:

2x(-9x+12)=-9

We move all terms to the left:

2x(-9x+12)-(-9)=0

We add all the numbers together, and all the variables

2x(-9x+12)+9=0

We multiply parentheses

-18x^2+24x+9=0

a = -18; b = 24; c = +9;
Δ = b2-4ac
Δ = 242-4·(-18)·9
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{34}}{2*-18}=\frac{-24-6\sqrt{34}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{34}}{2*-18}=\frac{-24+6\sqrt{34}}{-36}
$