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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


15x/75x^2+10x/75x^2+2+1=0

We add all the numbers together, and all the variables

15x/75x^2+10x/75x^2+3=0

We multiply all the terms by the denominator


15x+10x+3*75x^2=0

We add all the numbers together, and all the variables

25x+3*75x^2=0

Wy multiply elements

225x^2+25x=0

a = 225; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·225·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*225}=\frac{-50}{450}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*225}=\frac{0}{450}
=0
$