2/5x-1/15=5/2x

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

2/5x-1/15=5/2x

We move all terms to the left:

2/5x-1/15-(5/2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-20x^2)/150x^2+60x/150x^2+(-375x)/150x^2=0

We multiply all the terms by the denominator


(-20x^2)+60x+(-375x)=0

We get rid of parentheses

-20x^2+60x-375x=0

We add all the numbers together, and all the variables

-20x^2-315x=0

a = -20; b = -315; c = 0;
Δ = b2-4ac
Δ = -3152-4·(-20)·0
Δ = 99225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{99225}=315$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-315)-315}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-315)+315}{2*-20}=\frac{630}{-40}
=-15+3/4
$