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X^2-250X-12500=0
a = 1; b = -250; c = -12500;
Δ = b2-4ac
Δ = -2502-4·1·(-12500)
Δ = 112500
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{112500}=\sqrt{22500*5}=\sqrt{22500}*\sqrt{5}=150\sqrt{5}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-150\sqrt{5}}{2*1}=\frac{250-150\sqrt{5}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+150\sqrt{5}}{2*1}=\frac{250+150\sqrt{5}}{2} $
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