3x-8/4x+1=2

Solution for 3x-8/4x+1=2 equation:

3x-8/4x+1=2

We move all terms to the left:

3x-8/4x+1-(2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3x-8/4x-1=0

We multiply all the terms by the denominator


3x*4x-1*4x-8=0

Wy multiply elements

12x^2-4x-8=0

a = 12; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·12·(-8)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-20}{2*12}=\frac{-16}{24}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+20}{2*12}=\frac{24}{24}
=1
$