x^2/x+6=36/x+6

Solution for x^2/x+6=36/x+6 equation:

x^2/x+6=36/x+6

We move all terms to the left:

x^2/x+6-(36/x+6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+6)!=0

x∈R


We get rid of parentheses

x^2/x-36/x-6+6=0

We multiply all the terms by the denominator


x^2-6*x+6*x-36=0

We add all the numbers together, and all the variables

x^2-36=0

a = 1; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·1·(-36)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*1}=\frac{12}{2}
=6
$