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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(-6/3x+7)-6=0

We get rid of parentheses

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

We calculate fractions


9x/15x^2+30x/15x^2-7-6=0

We add all the numbers together, and all the variables

9x/15x^2+30x/15x^2-13=0

We multiply all the terms by the denominator


9x+30x-13*15x^2=0

We add all the numbers together, and all the variables

39x-13*15x^2=0

Wy multiply elements

-195x^2+39x=0

a = -195; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-195)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*-195}=\frac{-78}{-390}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-195}=\frac{0}{-390}
=0
$