x^2-72x-672=0

Solution for x^2-72x-672=0 equation:

x^2-72x-672=0

a = 1; b = -72; c = -672;
Δ = b2-4ac
Δ = -722-4·1·(-672)
Δ = 7872
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:

$\sqrt{\Delta}=\sqrt{7872}=\sqrt{64*123}=\sqrt{64}*\sqrt{123}=8\sqrt{123}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{123}}{2*1}=\frac{72-8\sqrt{123}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{123}}{2*1}=\frac{72+8\sqrt{123}}{2}
$