4/3x+2=7/5x

Solution for 4/3x+2=7/5x equation:

4/3x+2=7/5x

We move all terms to the left:

4/3x+2-(7/5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(+7/5x)+2=0

We get rid of parentheses

4/3x-7/5x+2=0

We calculate fractions


20x/15x^2+(-21x)/15x^2+2=0

We multiply all the terms by the denominator


20x+(-21x)+2*15x^2=0

Wy multiply elements

30x^2+20x+(-21x)=0

We get rid of parentheses

30x^2+20x-21x=0

We add all the numbers together, and all the variables

30x^2-1x=0

a = 30; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·30·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*30}=\frac{2}{60}
=1/30
$