36a/9a-24=9a+24

Solution for 36a/9a-24=9a+24 equation:

36a/9a-24=9a+24

We move all terms to the left:

36a/9a-24-(9a+24)=0


Domain of the equation: 9a!=0

a!=0/9

a!=0

a∈R


We get rid of parentheses

36a/9a-9a-24-24=0

We multiply all the terms by the denominator


36a-9a*9a-24*9a-24*9a=0

Wy multiply elements

-81a^2+36a-216a-216a=0

We add all the numbers together, and all the variables

-81a^2-396a=0

a = -81; b = -396; c = 0;
Δ = b2-4ac
Δ = -3962-4·(-81)·0
Δ = 156816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{156816}=396$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-396}{2*-81}=\frac{0}{-162}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+396}{2*-81}=\frac{792}{-162}
=-4+8/9
$