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6y^2-31y-7=0
a = 6; b = -31; c = -7;
Δ = b2-4ac
Δ = -312-4·6·(-7)
Δ = 1129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{1129}}{2*6}=\frac{31-\sqrt{1129}}{12} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1129}}{2*6}=\frac{31+\sqrt{1129}}{12} $
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