2x+12/4x=5x+8/4x+1

Solution for 2x+12/4x=5x+8/4x+1 equation:

2x+12/4x=5x+8/4x+1

We move all terms to the left:

2x+12/4x-(5x+8/4x+1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

2x+12/4x-5x-8/4x-1=0

We multiply all the terms by the denominator


2x*4x-5x*4x-1*4x+12-8=0

We add all the numbers together, and all the variables

2x*4x-5x*4x-1*4x+4=0

Wy multiply elements

8x^2-20x^2-4x+4=0

We add all the numbers together, and all the variables

-12x^2-4x+4=0

a = -12; b = -4; c = +4;
Δ = b2-4ac
Δ = -42-4·(-12)·4
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{13}}{2*-12}=\frac{4-4\sqrt{13}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{13}}{2*-12}=\frac{4+4\sqrt{13}}{-24}
$