12x-20+x^2=180

Solution for 12x-20+x^2=180 equation:

12x-20+x^2=180

We move all terms to the left:

12x-20+x^2-(180)=0

We add all the numbers together, and all the variables

x^2+12x-200=0

a = 1; b = 12; c = -200;
Δ = b2-4ac
Δ = 122-4·1·(-200)
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{59}}{2*1}=\frac{-12-4\sqrt{59}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{59}}{2*1}=\frac{-12+4\sqrt{59}}{2}
$