3/5x+2=1/3x-10

Solution for 3/5x+2=1/3x-10 equation:

3/5x+2=1/3x-10

We move all terms to the left:

3/5x+2-(1/3x-10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-10)!=0

x∈R


We get rid of parentheses

3/5x-1/3x+10+2=0

We calculate fractions


9x/15x^2+(-5x)/15x^2+10+2=0

We add all the numbers together, and all the variables

9x/15x^2+(-5x)/15x^2+12=0

We multiply all the terms by the denominator


9x+(-5x)+12*15x^2=0

Wy multiply elements

180x^2+9x+(-5x)=0

We get rid of parentheses

180x^2+9x-5x=0

We add all the numbers together, and all the variables

180x^2+4x=0

a = 180; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·180·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*180}=\frac{-8}{360}
=-1/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*180}=\frac{0}{360}
=0
$