X+5=1/36x

Solution for X+5=1/36x equation:

X+5=1/36X

We move all terms to the left:

X+5-(1/36X)=0


Domain of the equation: 36X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+1/36X)+5=0

We get rid of parentheses

X-1/36X+5=0

We multiply all the terms by the denominator


X*36X+5*36X-1=0

Wy multiply elements

36X^2+180X-1=0

a = 36; b = 180; c = -1;
Δ = b2-4ac
Δ = 1802-4·36·(-1)
Δ = 32544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32544}=\sqrt{144*226}=\sqrt{144}*\sqrt{226}=12\sqrt{226}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{226}}{2*36}=\frac{-180-12\sqrt{226}}{72}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{226}}{2*36}=\frac{-180+12\sqrt{226}}{72}
$