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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-36x^2)/48x^2+36x/48x^2+(-32x)/48x^2+2=0

We multiply all the terms by the denominator


(-36x^2)+36x+(-32x)+2*48x^2=0

Wy multiply elements

(-36x^2)+96x^2+36x+(-32x)=0

We get rid of parentheses

-36x^2+96x^2+36x-32x=0

We add all the numbers together, and all the variables

60x^2+4x=0

a = 60; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·60·0
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*60}=\frac{-8}{120}
=-1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*60}=\frac{0}{120}
=0
$