9a-6=3-6/4a

Solution for 9a-6=3-6/4a equation:

9a-6=3-6/4a

We move all terms to the left:

9a-6-(3-6/4a)=0


Domain of the equation: 4a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

9a-(-6/4a+3)-6=0

We get rid of parentheses

9a+6/4a-3-6=0

We multiply all the terms by the denominator


9a*4a-3*4a-6*4a+6=0

Wy multiply elements

36a^2-12a-24a+6=0

We add all the numbers together, and all the variables

36a^2-36a+6=0

a = 36; b = -36; c = +6;
Δ = b2-4ac
Δ = -362-4·36·6
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{3}}{2*36}=\frac{36-12\sqrt{3}}{72}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{3}}{2*36}=\frac{36+12\sqrt{3}}{72}
$