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6a^2+31a-10=0
a = 6; b = 31; c = -10;
Δ = b2-4ac
Δ = 312-4·6·(-10)
Δ = 1201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{1201}}{2*6}=\frac{-31-\sqrt{1201}}{12} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{1201}}{2*6}=\frac{-31+\sqrt{1201}}{12} $
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