9a-36/(a+2)=0

Solution for 9a-36/(a+2)=0 equation:

9a-36/(a+2)=0


Domain of the equation: (a+2)!=0

We move all terms containing a to the left, all other terms to the right

a!=-2

a∈R


We multiply all the terms by the denominator


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}
$