2/15x-1/3=4/5x+2

Solution for 2/15x-1/3=4/5x+2 equation:

2/15x-1/3=4/5x+2

We move all terms to the left:

2/15x-1/3-(4/5x+2)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R



Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

2/15x-4/5x-2-1/3=0

We calculate fractions


(-375x^2)/675x^2+90x/675x^2+(-540x)/675x^2-2=0

We multiply all the terms by the denominator


(-375x^2)+90x+(-540x)-2*675x^2=0

Wy multiply elements

(-375x^2)-1350x^2+90x+(-540x)=0

We get rid of parentheses

-375x^2-1350x^2+90x-540x=0

We add all the numbers together, and all the variables

-1725x^2-450x=0

a = -1725; b = -450; c = 0;
Δ = b2-4ac
Δ = -4502-4·(-1725)·0
Δ = 202500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{202500}=450$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-450}{2*-1725}=\frac{0}{-3450}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+450}{2*-1725}=\frac{900}{-3450}
=-6/23
$