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X^2-31X-180=0
a = 1; b = -31; c = -180;
Δ = b2-4ac
Δ = -312-4·1·(-180)
Δ = 1681
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1681}=41$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-41}{2*1}=\frac{-10}{2} =-5 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+41}{2*1}=\frac{72}{2} =36 $
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