3/4x+1/5=2/3x

Solution for 3/4x+1/5=2/3x equation:

3/4x+1/5=2/3x

We move all terms to the left:

3/4x+1/5-(2/3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(+2/3x)+1/5=0

We get rid of parentheses

3/4x-2/3x+1/5=0

We calculate fractions


36x^2/300x^2+225x/300x^2+(-200x)/300x^2=0

We multiply all the terms by the denominator


36x^2+225x+(-200x)=0

We get rid of parentheses

36x^2+225x-200x=0

We add all the numbers together, and all the variables

36x^2+25x=0

a = 36; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·36·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*36}=\frac{-50}{72}
=-25/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*36}=\frac{0}{72}
=0
$