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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


3x/6x^2+(-8x)/6x^2-1-2=0

We add all the numbers together, and all the variables

3x/6x^2+(-8x)/6x^2-3=0

We multiply all the terms by the denominator


3x+(-8x)-3*6x^2=0

Wy multiply elements

-18x^2+3x+(-8x)=0

We get rid of parentheses

-18x^2+3x-8x=0

We add all the numbers together, and all the variables

-18x^2-5x=0

a = -18; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-18)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-18}=\frac{10}{-36}
=-5/18
$