X^2+24x+144=20

Solution for X^2+24x+144=20 equation:

X^2+24X+144=20

We move all terms to the left:

X^2+24X+144-(20)=0

We add all the numbers together, and all the variables

X^2+24X+124=0

a = 1; b = 24; c = +124;
Δ = b2-4ac
Δ = 242-4·1·124
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{5}}{2*1}=\frac{-24-4\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{5}}{2*1}=\frac{-24+4\sqrt{5}}{2}
$