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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


12x/20x^2+(-15x)/20x^2+2-5=0

We add all the numbers together, and all the variables

12x/20x^2+(-15x)/20x^2-3=0

We multiply all the terms by the denominator


12x+(-15x)-3*20x^2=0

Wy multiply elements

-60x^2+12x+(-15x)=0

We get rid of parentheses

-60x^2+12x-15x=0

We add all the numbers together, and all the variables

-60x^2-3x=0

a = -60; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-60)·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*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-60}=\frac{6}{-120}
=-1/20
$