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5x^2-125x-250=0
a = 5; b = -125; c = -250;
Δ = b2-4ac
Δ = -1252-4·5·(-250)
Δ = 20625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20625}=\sqrt{625*33}=\sqrt{625}*\sqrt{33}=25\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-125)-25\sqrt{33}}{2*5}=\frac{125-25\sqrt{33}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+25\sqrt{33}}{2*5}=\frac{125+25\sqrt{33}}{10} $
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