5/2x+3/5=3/10x

Solution for 5/2x+3/5=3/10x equation:

5/2x+3/5=3/10x

We move all terms to the left:

5/2x+3/5-(3/10x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-(+3/10x)+3/5=0

We get rid of parentheses

5/2x-3/10x+3/5=0

We calculate fractions


60x^2/500x^2+1250x/500x^2+(-150x)/500x^2=0

We multiply all the terms by the denominator


60x^2+1250x+(-150x)=0

We get rid of parentheses

60x^2+1250x-150x=0

We add all the numbers together, and all the variables

60x^2+1100x=0

a = 60; b = 1100; c = 0;
Δ = b2-4ac
Δ = 11002-4·60·0
Δ = 1210000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1210000}=1100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1100)-1100}{2*60}=\frac{-2200}{120}
=-18+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1100)+1100}{2*60}=\frac{0}{120}
=0
$