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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


64x^2/72x^2+36x/72x^2+(-54x)/72x^2+2=0

We multiply all the terms by the denominator


64x^2+36x+(-54x)+2*72x^2=0

Wy multiply elements

64x^2+144x^2+36x+(-54x)=0

We get rid of parentheses

64x^2+144x^2+36x-54x=0

We add all the numbers together, and all the variables

208x^2-18x=0

a = 208; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·208·0
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*208}=\frac{0}{416}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*208}=\frac{36}{416}
=9/104
$