3/2x-6=3/5x+4

Solution for 3/2x-6=3/5x+4 equation:

3/2x-6=3/5x+4

We move all terms to the left:

3/2x-6-(3/5x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

3/2x-3/5x-4-6=0

We calculate fractions


15x/10x^2+(-6x)/10x^2-4-6=0

We add all the numbers together, and all the variables

15x/10x^2+(-6x)/10x^2-10=0

We multiply all the terms by the denominator


15x+(-6x)-10*10x^2=0

Wy multiply elements

-100x^2+15x+(-6x)=0

We get rid of parentheses

-100x^2+15x-6x=0

We add all the numbers together, and all the variables

-100x^2+9x=0

a = -100; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-100)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-100}=\frac{-18}{-200}
=9/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-100}=\frac{0}{-200}
=0
$