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x^2-100x+576=0
a = 1; b = -100; c = +576;
Δ = b2-4ac
Δ = -1002-4·1·576
Δ = 7696
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7696}=\sqrt{16*481}=\sqrt{16}*\sqrt{481}=4\sqrt{481}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{481}}{2*1}=\frac{100-4\sqrt{481}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{481}}{2*1}=\frac{100+4\sqrt{481}}{2} $
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