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X^2+200X-15540=0
a = 1; b = 200; c = -15540;
Δ = b2-4ac
Δ = 2002-4·1·(-15540)
Δ = 102160
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{102160}=\sqrt{16*6385}=\sqrt{16}*\sqrt{6385}=4\sqrt{6385}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-4\sqrt{6385}}{2*1}=\frac{-200-4\sqrt{6385}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+4\sqrt{6385}}{2*1}=\frac{-200+4\sqrt{6385}}{2} $
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