X^2-4x+12=180

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

X^2-4X+12=180

We move all terms to the left:

X^2-4X+12-(180)=0

We add all the numbers together, and all the variables

X^2-4X-168=0

a = 1; b = -4; c = -168;
Δ = b2-4ac
Δ = -42-4·1·(-168)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{43}}{2*1}=\frac{4-4\sqrt{43}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{43}}{2*1}=\frac{4+4\sqrt{43}}{2}
$