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=-16Y^2+18Y+5
We move all terms to the left:
-(-16Y^2+18Y+5)=0
We get rid of parentheses
16Y^2-18Y-5=0
a = 16; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·16·(-5)
Δ = 644
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{161}}{2*16}=\frac{18-2\sqrt{161}}{32} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{161}}{2*16}=\frac{18+2\sqrt{161}}{32} $
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