x^2-96x+576=0

Solution for x^2-96x+576=0 equation:

x^2-96x+576=0

a = 1; b = -96; c = +576;
Δ = b2-4ac
Δ = -962-4·1·576
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-48\sqrt{3}}{2*1}=\frac{96-48\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+48\sqrt{3}}{2*1}=\frac{96+48\sqrt{3}}{2}
$