X^2-72x+1200=0

Solution for X^2-72x+1200=0 equation:

X^2-72X+1200=0

a = 1; b = -72; c = +1200;
Δ = b2-4ac
Δ = -722-4·1·1200
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{6}}{2*1}=\frac{72-8\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{6}}{2*1}=\frac{72+8\sqrt{6}}{2}
$