3/4x-1/5=6/5x+1

Solution for 3/4x-1/5=6/5x+1 equation:

3/4x-1/5=6/5x+1

We move all terms to the left:

3/4x-1/5-(6/5x+1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x+1)!=0

x∈R


We get rid of parentheses

3/4x-6/5x-1-1/5=0

We calculate fractions


375x/500x^2+(-24x)/500x^2+(-4x)/500x^2-1=0

We multiply all the terms by the denominator


375x+(-24x)+(-4x)-1*500x^2=0

Wy multiply elements

-500x^2+375x+(-24x)+(-4x)=0

We get rid of parentheses

-500x^2+375x-24x-4x=0

We add all the numbers together, and all the variables

-500x^2+347x=0

a = -500; b = 347; c = 0;
Δ = b2-4ac
Δ = 3472-4·(-500)·0
Δ = 120409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{120409}=347$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(347)-347}{2*-500}=\frac{-694}{-1000}
=347/500
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(347)+347}{2*-500}=\frac{0}{-1000}
=0
$