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=9Y^2+18Y+4
We move all terms to the left:
-(9Y^2+18Y+4)=0
We get rid of parentheses
-9Y^2-18Y-4=0
a = -9; b = -18; c = -4;
Δ = b2-4ac
Δ = -182-4·(-9)·(-4)
Δ = 180
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{5}}{2*-9}=\frac{18-6\sqrt{5}}{-18} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{5}}{2*-9}=\frac{18+6\sqrt{5}}{-18} $
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