12x-18+2x^2=180

Solution for 12x-18+2x^2=180 equation:

12x-18+2x^2=180

We move all terms to the left:

12x-18+2x^2-(180)=0

We add all the numbers together, and all the variables

2x^2+12x-198=0

a = 2; b = 12; c = -198;
Δ = b2-4ac
Δ = 122-4·2·(-198)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24\sqrt{3}}{2*2}=\frac{-12-24\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24\sqrt{3}}{2*2}=\frac{-12+24\sqrt{3}}{4}
$