x^2+72x+144=0

Solution for x^2+72x+144=0 equation:

x^2+72x+144=0

a = 1; b = 72; c = +144;
Δ = b2-4ac
Δ = 722-4·1·144
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-48\sqrt{2}}{2*1}=\frac{-72-48\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+48\sqrt{2}}{2*1}=\frac{-72+48\sqrt{2}}{2}
$