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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


12x/32x^2+(-24x)/32x^2+(-4x)/32x^2-3=0

We multiply all the terms by the denominator


12x+(-24x)+(-4x)-3*32x^2=0

Wy multiply elements

-96x^2+12x+(-24x)+(-4x)=0

We get rid of parentheses

-96x^2+12x-24x-4x=0

We add all the numbers together, and all the variables

-96x^2-16x=0

a = -96; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-96)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-96}=\frac{0}{-192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-96}=\frac{32}{-192}
=-1/6
$