/(x^2-36)=8

Solution for /(x^2-36)=8 equation:

/(x^2-36)=8

We move all terms to the left:

/(x^2-36)-(8)=0


Domain of the equation: (x^2-36)!=0

We move all terms containing x to the left, all other terms to the right

x^2!=36

x^2!=36/

x^2!=√1/0

x!=1

x∈R


We multiply all the terms by the denominator


-8*(x^2-36)+=0

We add all the numbers together, and all the variables

-8*(x^2-36)=0

We multiply parentheses

-8x^2+288=0

a = -8; b = 0; c = +288;
Δ = b2-4ac
Δ = 02-4·(-8)·288
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96}{2*-8}=\frac{-96}{-16}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96}{2*-8}=\frac{96}{-16}
=-6
$