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=-Y^2+6Y+30
We move all terms to the left:
-(-Y^2+6Y+30)=0
We get rid of parentheses
Y^2-6Y-30=0
a = 1; b = -6; c = -30;
Δ = b2-4ac
Δ = -62-4·1·(-30)
Δ = 156
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*1}=\frac{6-2\sqrt{39}}{2} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*1}=\frac{6+2\sqrt{39}}{2} $
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