x=36/x+5

Solution for x=36/x+5 equation:

x=36/x+5

We move all terms to the left:

x-(36/x+5)=0


Domain of the equation: x+5)!=0

x∈R


We get rid of parentheses

x-36/x-5=0

We multiply all the terms by the denominator


x*x-5*x-36=0

We add all the numbers together, and all the variables

-5x+x*x-36=0

Wy multiply elements

x^2-5x-36=0

a = 1; b = -5; c = -36;
Δ = b2-4ac
Δ = -52-4·1·(-36)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*1}=\frac{18}{2}
=9
$