180=8x^2-4x+12

Solution for 180=8x^2-4x+12 equation:

180=8x^2-4x+12

We move all terms to the left:

180-(8x^2-4x+12)=0

We get rid of parentheses

-8x^2+4x-12+180=0

We add all the numbers together, and all the variables

-8x^2+4x+168=0

a = -8; b = 4; c = +168;
Δ = b2-4ac
Δ = 42-4·(-8)·168
Δ = 5392
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:

$\sqrt{\Delta}=\sqrt{5392}=\sqrt{16*337}=\sqrt{16}*\sqrt{337}=4\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{337}}{2*-8}=\frac{-4-4\sqrt{337}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{337}}{2*-8}=\frac{-4+4\sqrt{337}}{-16}
$