x^2+24x+36=240

Solution for x^2+24x+36=240 equation:

x^2+24x+36=240

We move all terms to the left:

x^2+24x+36-(240)=0

We add all the numbers together, and all the variables

x^2+24x-204=0

a = 1; b = 24; c = -204;
Δ = b2-4ac
Δ = 242-4·1·(-204)
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{87}}{2*1}=\frac{-24-4\sqrt{87}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{87}}{2*1}=\frac{-24+4\sqrt{87}}{2}
$