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y^2-7y-31=0
a = 1; b = -7; c = -31;
Δ = b2-4ac
Δ = -72-4·1·(-31)
Δ = 173
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{-(-7)-\sqrt{173}}{2*1}=\frac{7-\sqrt{173}}{2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{173}}{2*1}=\frac{7+\sqrt{173}}{2} $
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