x^2+2x-24=180

Solution for x^2+2x-24=180 equation:

x^2+2x-24=180

We move all terms to the left:

x^2+2x-24-(180)=0

We add all the numbers together, and all the variables

x^2+2x-204=0

a = 1; b = 2; c = -204;
Δ = b2-4ac
Δ = 22-4·1·(-204)
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{205}}{2*1}=\frac{-2-2\sqrt{205}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{205}}{2*1}=\frac{-2+2\sqrt{205}}{2}
$