5/2x+10=5/3x

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

5/2x+10=5/3x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


15x/6x^2+(-10x)/6x^2+10=0

We multiply all the terms by the denominator


15x+(-10x)+10*6x^2=0

Wy multiply elements

60x^2+15x+(-10x)=0

We get rid of parentheses

60x^2+15x-10x=0

We add all the numbers together, and all the variables

60x^2+5x=0

a = 60; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·60·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*60}=\frac{-10}{120}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*60}=\frac{0}{120}
=0
$