x^2-72x-500=0

Solution for x^2-72x-500=0 equation:

x^2-72x-500=0

a = 1; b = -72; c = -500;
Δ = b2-4ac
Δ = -722-4·1·(-500)
Δ = 7184
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:

$\sqrt{\Delta}=\sqrt{7184}=\sqrt{16*449}=\sqrt{16}*\sqrt{449}=4\sqrt{449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{449}}{2*1}=\frac{72-4\sqrt{449}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{449}}{2*1}=\frac{72+4\sqrt{449}}{2}
$