(5+x)=36/x

Solution for (5+x)=36/x equation:

(5+x)=36/x

We move all terms to the left:

(5+x)-(36/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(x+5)-(+36/x)=0

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