X^2+72x-1600=0

Solution for X^2+72x-1600=0 equation:

X^2+72X-1600=0

a = 1; b = 72; c = -1600;
Δ = b2-4ac
Δ = 722-4·1·(-1600)
Δ = 11584
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:

$\sqrt{\Delta}=\sqrt{11584}=\sqrt{64*181}=\sqrt{64}*\sqrt{181}=8\sqrt{181}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-8\sqrt{181}}{2*1}=\frac{-72-8\sqrt{181}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+8\sqrt{181}}{2*1}=\frac{-72+8\sqrt{181}}{2}
$