12/(2x^2+2x-1)=12

Solution for 12/(2x^2+2x-1)=12 equation:

12/(2x^2+2x-1)=12

We move all terms to the left:

12/(2x^2+2x-1)-(12)=0


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

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

2x^2+2x!=1

x∈R


We multiply all the terms by the denominator


-12*(2x^2+2x-1)+12=0

We multiply parentheses

-24x^2-24x+12+12=0

We add all the numbers together, and all the variables

-24x^2-24x+24=0

a = -24; b = -24; c = +24;
Δ = b2-4ac
Δ = -242-4·(-24)·24
Δ = 2880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{5}}{2*-24}=\frac{24-24\sqrt{5}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{5}}{2*-24}=\frac{24+24\sqrt{5}}{-48}
$