-2x^2+18=12x

Solution for -2x^2+18=12x equation:

-2x^2+18=12x

We move all terms to the left:

-2x^2+18-(12x)=0

a = -2; b = -12; c = +18;
Δ = b2-4ac
Δ = -122-4·(-2)·18
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{2}}{2*-2}=\frac{12-12\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{2}}{2*-2}=\frac{12+12\sqrt{2}}{-4}
$