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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-16x^2)/72x^2+54x/72x^2+(-36x)/72x^2-2=0

We multiply all the terms by the denominator


(-16x^2)+54x+(-36x)-2*72x^2=0

Wy multiply elements

(-16x^2)-144x^2+54x+(-36x)=0

We get rid of parentheses

-16x^2-144x^2+54x-36x=0

We add all the numbers together, and all the variables

-160x^2+18x=0

a = -160; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-160)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-160}=\frac{-36}{-320}
=9/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-160}=\frac{0}{-320}
=0
$