2/3x-1/3=7/5x+5

Solution for 2/3x-1/3=7/5x+5 equation:

2/3x-1/3=7/5x+5

We move all terms to the left:

2/3x-1/3-(7/5x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

2/3x-7/5x-5-1/3=0

We calculate fractions


10x/135x^2+(-189x)/135x^2+(-5x)/135x^2-5=0

We multiply all the terms by the denominator


10x+(-189x)+(-5x)-5*135x^2=0

Wy multiply elements

-675x^2+10x+(-189x)+(-5x)=0

We get rid of parentheses

-675x^2+10x-189x-5x=0

We add all the numbers together, and all the variables

-675x^2-184x=0

a = -675; b = -184; c = 0;
Δ = b2-4ac
Δ = -1842-4·(-675)·0
Δ = 33856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33856}=184$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-184}{2*-675}=\frac{0}{-1350}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+184}{2*-675}=\frac{368}{-1350}
=-184/675
$