3/2x-1=8/4x+5

Solution for 3/2x-1=8/4x+5 equation:

3/2x-1=8/4x+5

We move all terms to the left:

3/2x-1-(8/4x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

3/2x-8/4x-5-1=0

We calculate fractions


12x/8x^2+(-16x)/8x^2-5-1=0

We add all the numbers together, and all the variables

12x/8x^2+(-16x)/8x^2-6=0

We multiply all the terms by the denominator


12x+(-16x)-6*8x^2=0

Wy multiply elements

-48x^2+12x+(-16x)=0

We get rid of parentheses

-48x^2+12x-16x=0

We add all the numbers together, and all the variables

-48x^2-4x=0

a = -48; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-48)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-48}=\frac{8}{-96}
=-1/12
$