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6x^2-31x-3=0
a = 6; b = -31; c = -3;
Δ = b2-4ac
Δ = -312-4·6·(-3)
Δ = 1033
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{1033}}{2*6}=\frac{31-\sqrt{1033}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1033}}{2*6}=\frac{31+\sqrt{1033}}{12} $
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