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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


15x/20x^2+(-12x)/20x^2-2-4=0

We add all the numbers together, and all the variables

15x/20x^2+(-12x)/20x^2-6=0

We multiply all the terms by the denominator


15x+(-12x)-6*20x^2=0

Wy multiply elements

-120x^2+15x+(-12x)=0

We get rid of parentheses

-120x^2+15x-12x=0

We add all the numbers together, and all the variables

-120x^2+3x=0

a = -120; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-120)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-120}=\frac{-6}{-240}
=1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-120}=\frac{0}{-240}
=0
$