x^2-72x+99=0

Solution for x^2-72x+99=0 equation:

x^2-72x+99=0

a = 1; b = -72; c = +99;
Δ = b2-4ac
Δ = -722-4·1·99
Δ = 4788
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:

$\sqrt{\Delta}=\sqrt{4788}=\sqrt{36*133}=\sqrt{36}*\sqrt{133}=6\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-6\sqrt{133}}{2*1}=\frac{72-6\sqrt{133}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+6\sqrt{133}}{2*1}=\frac{72+6\sqrt{133}}{2}
$