x^2-84x+576=0

Solution for x^2-84x+576=0 equation:

x^2-84x+576=0

a = 1; b = -84; c = +576;
Δ = b2-4ac
Δ = -842-4·1·576
Δ = 4752
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:

$\sqrt{\Delta}=\sqrt{4752}=\sqrt{144*33}=\sqrt{144}*\sqrt{33}=12\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{33}}{2*1}=\frac{84-12\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{33}}{2*1}=\frac{84+12\sqrt{33}}{2}
$