((9x^2)-1)/(6x+2)=13

Solution for ((9x^2)-1)/(6x+2)=13 equation:

((9x^2)-1)/(6x+2)=13

We move all terms to the left:

((9x^2)-1)/(6x+2)-(13)=0


Domain of the equation: (6x+2)!=0

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

6x!=-2

x!=-2/6

x!=-1/3

x∈R


We multiply all the terms by the denominator


(9x^2-1)-13*(6x+2)=0

We multiply parentheses

(9x^2-1)-78x-26=0

We get rid of parentheses

9x^2-78x-1-26=0

We add all the numbers together, and all the variables

9x^2-78x-27=0

a = 9; b = -78; c = -27;
Δ = b2-4ac
Δ = -782-4·9·(-27)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-84}{2*9}=\frac{-6}{18}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+84}{2*9}=\frac{162}{18}
=9
$