36/x=13-x

Solution for 36/x=13-x equation:

36/x=13-x

We move all terms to the left:

36/x-(13-x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

36/x-(-1x+13)=0

We get rid of parentheses

36/x+1x-13=0

We multiply all the terms by the denominator


1x*x-13*x+36=0

We add all the numbers together, and all the variables

-13x+1x*x+36=0

Wy multiply elements

x^2-13x+36=0

a = 1; b = -13; c = +36;
Δ = b2-4ac
Δ = -132-4·1·36
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{-(-13)-5}{2*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*1}=\frac{18}{2}
=9
$