1/5x-5=13-1/10x

Solution for 1/5x-5=13-1/10x equation:

1/5x-5=13-1/10x

We move all terms to the left:

1/5x-5-(13-1/10x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(-1/10x+13)-5=0

We get rid of parentheses

1/5x+1/10x-13-5=0

We calculate fractions


10x/50x^2+5x/50x^2-13-5=0

We add all the numbers together, and all the variables

10x/50x^2+5x/50x^2-18=0

We multiply all the terms by the denominator


10x+5x-18*50x^2=0

We add all the numbers together, and all the variables

15x-18*50x^2=0

Wy multiply elements

-900x^2+15x=0

a = -900; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-900)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-900}=\frac{-30}{-1800}
=1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-900}=\frac{0}{-1800}
=0
$