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9y^2+54y+8=81
We move all terms to the left:
9y^2+54y+8-(81)=0
We add all the numbers together, and all the variables
9y^2+54y-73=0
a = 9; b = 54; c = -73;
Δ = b2-4ac
Δ = 542-4·9·(-73)
Δ = 5544
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5544}=\sqrt{36*154}=\sqrt{36}*\sqrt{154}=6\sqrt{154}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{154}}{2*9}=\frac{-54-6\sqrt{154}}{18} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{154}}{2*9}=\frac{-54+6\sqrt{154}}{18} $
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