1/10x+15=1/15x+10

Solution for 1/10x+15=1/15x+10 equation:

1/10x+15=1/15x+10

We move all terms to the left:

1/10x+15-(1/15x+10)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 15x+10)!=0

x∈R


We get rid of parentheses

1/10x-1/15x-10+15=0

We calculate fractions


15x/150x^2+(-10x)/150x^2-10+15=0

We add all the numbers together, and all the variables

15x/150x^2+(-10x)/150x^2+5=0

We multiply all the terms by the denominator


15x+(-10x)+5*150x^2=0

Wy multiply elements

750x^2+15x+(-10x)=0

We get rid of parentheses

750x^2+15x-10x=0

We add all the numbers together, and all the variables

750x^2+5x=0

a = 750; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·750·0
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*750}=\frac{-10}{1500}
=-1/150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*750}=\frac{0}{1500}
=0
$