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9a-36/(a+2)=0
Domain of the equation: (a+2)!=0We multiply all the terms by the denominator
We move all terms containing a to the left, all other terms to the right
a!=-2
a∈R
9a*(a+2)-36=0
We multiply parentheses
9a^2+18a-36=0
a = 9; b = 18; c = -36;
Δ = b2-4ac
Δ = 182-4·9·(-36)
Δ = 1620
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18\sqrt{5}}{2*9}=\frac{-18-18\sqrt{5}}{18} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18\sqrt{5}}{2*9}=\frac{-18+18\sqrt{5}}{18} $
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