12/15x-10=2/3x

Solution for 12/15x-10=2/3x equation:

12/15x-10=2/3x

We move all terms to the left:

12/15x-10-(2/3x)=0


Domain of the equation: 15x!=0

x!=0/15

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

12/15x-(+2/3x)-10=0

We get rid of parentheses

12/15x-2/3x-10=0

We calculate fractions


36x/45x^2+(-30x)/45x^2-10=0

We multiply all the terms by the denominator


36x+(-30x)-10*45x^2=0

Wy multiply elements

-450x^2+36x+(-30x)=0

We get rid of parentheses

-450x^2+36x-30x=0

We add all the numbers together, and all the variables

-450x^2+6x=0

a = -450; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-450)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-450}=\frac{-12}{-900}
=1/75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-450}=\frac{0}{-900}
=0
$