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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


9x/15x^2+10x/15x^2+3-6=0

We add all the numbers together, and all the variables

9x/15x^2+10x/15x^2-3=0

We multiply all the terms by the denominator


9x+10x-3*15x^2=0

We add all the numbers together, and all the variables

19x-3*15x^2=0

Wy multiply elements

-45x^2+19x=0

a = -45; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-45)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-45}=\frac{-38}{-90}
=19/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-45}=\frac{0}{-90}
=0
$