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=2-9Y^2+54Y
We move all terms to the left:
-(2-9Y^2+54Y)=0
We get rid of parentheses
9Y^2-54Y-2=0
a = 9; b = -54; c = -2;
Δ = b2-4ac
Δ = -542-4·9·(-2)
Δ = 2988
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2988}=\sqrt{36*83}=\sqrt{36}*\sqrt{83}=6\sqrt{83}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{83}}{2*9}=\frac{54-6\sqrt{83}}{18} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{83}}{2*9}=\frac{54+6\sqrt{83}}{18} $
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