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y^2+250y-75000=0
a = 1; b = 250; c = -75000;
Δ = b2-4ac
Δ = 2502-4·1·(-75000)
Δ = 362500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{362500}=\sqrt{2500*145}=\sqrt{2500}*\sqrt{145}=50\sqrt{145}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-50\sqrt{145}}{2*1}=\frac{-250-50\sqrt{145}}{2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+50\sqrt{145}}{2*1}=\frac{-250+50\sqrt{145}}{2} $
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