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=-2Y^2+36Y+6
We move all terms to the left:
-(-2Y^2+36Y+6)=0
We get rid of parentheses
2Y^2-36Y-6=0
a = 2; b = -36; c = -6;
Δ = b2-4ac
Δ = -362-4·2·(-6)
Δ = 1344
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{21}}{2*2}=\frac{36-8\sqrt{21}}{4} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{21}}{2*2}=\frac{36+8\sqrt{21}}{4} $
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