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6y^2-32y-31=0
a = 6; b = -32; c = -31;
Δ = b2-4ac
Δ = -322-4·6·(-31)
Δ = 1768
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1768}=\sqrt{4*442}=\sqrt{4}*\sqrt{442}=2\sqrt{442}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{442}}{2*6}=\frac{32-2\sqrt{442}}{12} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{442}}{2*6}=\frac{32+2\sqrt{442}}{12} $
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