7/3x-2/3=-6/5x-1

Solution for 7/3x-2/3=-6/5x-1 equation:

7/3x-2/3=-6/5x-1

We move all terms to the left:

7/3x-2/3-(-6/5x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

7/3x+6/5x+1-2/3=0

We calculate fractions


35x/135x^2+162x/135x^2+(-10x)/135x^2+1=0

We multiply all the terms by the denominator


35x+162x+(-10x)+1*135x^2=0

We add all the numbers together, and all the variables

197x+(-10x)+1*135x^2=0

Wy multiply elements

135x^2+197x+(-10x)=0

We get rid of parentheses

135x^2+197x-10x=0

We add all the numbers together, and all the variables

135x^2+187x=0

a = 135; b = 187; c = 0;
Δ = b2-4ac
Δ = 1872-4·135·0
Δ = 34969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34969}=187$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(187)-187}{2*135}=\frac{-374}{270}
=-1+52/135
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(187)+187}{2*135}=\frac{0}{270}
=0
$