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X^2-31X+204=0
a = 1; b = -31; c = +204;
Δ = b2-4ac
Δ = -312-4·1·204
Δ = 145
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{145}}{2*1}=\frac{31-\sqrt{145}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{145}}{2*1}=\frac{31+\sqrt{145}}{2} $
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