x^2-72x+105=0

Solution for x^2-72x+105=0 equation:

x^2-72x+105=0

a = 1; b = -72; c = +105;
Δ = b2-4ac
Δ = -722-4·1·105
Δ = 4764
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:

$\sqrt{\Delta}=\sqrt{4764}=\sqrt{4*1191}=\sqrt{4}*\sqrt{1191}=2\sqrt{1191}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1191}}{2*1}=\frac{72-2\sqrt{1191}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1191}}{2*1}=\frac{72+2\sqrt{1191}}{2}
$