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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-60x^2+15x-12x=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{-6}{-120}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-60}=\frac{0}{-120}
=0
$