1/5x+5=1/10x-15

Solution for 1/5x+5=1/10x-15 equation:

1/5x+5=1/10x-15

We move all terms to the left:

1/5x+5-(1/10x-15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/5x-1/10x+15+5=0

We calculate fractions


10x/50x^2+(-5x)/50x^2+15+5=0

We add all the numbers together, and all the variables

10x/50x^2+(-5x)/50x^2+20=0

We multiply all the terms by the denominator


10x+(-5x)+20*50x^2=0

Wy multiply elements

1000x^2+10x+(-5x)=0

We get rid of parentheses

1000x^2+10x-5x=0

We add all the numbers together, and all the variables

1000x^2+5x=0

a = 1000; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·1000·0
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*1000}=\frac{-10}{2000}
=-1/200
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*1000}=\frac{0}{2000}
=0
$