X^2-12+x^2-2x=180

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

X^2-12+X^2-2X=180

We move all terms to the left:

X^2-12+X^2-2X-(180)=0

We add all the numbers together, and all the variables

2X^2-2X-192=0

a = 2; b = -2; c = -192;
Δ = b2-4ac
Δ = -22-4·2·(-192)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{385}}{2*2}=\frac{2-2\sqrt{385}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{385}}{2*2}=\frac{2+2\sqrt{385}}{4}
$