(x/15)+13=(20/x)-2

Solution for (x/15)+13=(20/x)-2 equation:

(x/15)+13=(20/x)-2

We move all terms to the left:

(x/15)+13-((20/x)-2)=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+x/15)-((+20/x)-2)+13=0

We get rid of parentheses

x/15-((+20/x)-2)+13=0

We calculate fractions


x^2/15x+()/15x+13=0

We multiply all the terms by the denominator


x^2+13*15x+()=0

We add all the numbers together, and all the variables

x^2+13*15x=0

Wy multiply elements

x^2+195x=0

a = 1; b = 195; c = 0;
Δ = b2-4ac
Δ = 1952-4·1·0
Δ = 38025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38025}=195$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(195)-195}{2*1}=\frac{-390}{2}
=-195
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(195)+195}{2*1}=\frac{0}{2}
=0
$