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x^2-500x+900=0
a = 1; b = -500; c = +900;
Δ = b2-4ac
Δ = -5002-4·1·900
Δ = 246400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{246400}=\sqrt{1600*154}=\sqrt{1600}*\sqrt{154}=40\sqrt{154}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-40\sqrt{154}}{2*1}=\frac{500-40\sqrt{154}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+40\sqrt{154}}{2*1}=\frac{500+40\sqrt{154}}{2} $
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