2/3x-10=4/15x

Solution for 2/3x-10=4/15x equation:

2/3x-10=4/15x

We move all terms to the left:

2/3x-10-(4/15x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(+4/15x)-10=0

We get rid of parentheses

2/3x-4/15x-10=0

We calculate fractions


30x/45x^2+(-12x)/45x^2-10=0

We multiply all the terms by the denominator


30x+(-12x)-10*45x^2=0

Wy multiply elements

-450x^2+30x+(-12x)=0

We get rid of parentheses

-450x^2+30x-12x=0

We add all the numbers together, and all the variables

-450x^2+18x=0

a = -450; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-450)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-450}=\frac{-36}{-900}
=1/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-450}=\frac{0}{-900}
=0
$