((4x^2)-1)/(2x-1)=9

Solution for ((4x^2)-1)/(2x-1)=9 equation:

((4x^2)-1)/(2x-1)=9

We move all terms to the left:

((4x^2)-1)/(2x-1)-(9)=0


Domain of the equation: (2x-1)!=0

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

2x!=1

x!=1/2

x!=1/2

x∈R


We multiply all the terms by the denominator


(4x^2-1)-9*(2x-1)=0

We multiply parentheses

(4x^2-1)-18x+9=0

We get rid of parentheses

4x^2-18x-1+9=0

We add all the numbers together, and all the variables

4x^2-18x+8=0

a = 4; b = -18; c = +8;
Δ = b2-4ac
Δ = -182-4·4·8
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-14}{2*4}=\frac{4}{8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+14}{2*4}=\frac{32}{8}
=4
$