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-31x^2-62x+93=0
a = -31; b = -62; c = +93;
Δ = b2-4ac
Δ = -622-4·(-31)·93
Δ = 15376
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{15376}=124$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-124}{2*-31}=\frac{-62}{-62} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+124}{2*-31}=\frac{186}{-62} =-3 $
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