X+8=1/x-4

Solution for X+8=1/x-4 equation:

X+8=1/X-4

We move all terms to the left:

X+8-(1/X-4)=0


Domain of the equation: X-4)!=0

X∈R


We get rid of parentheses

X-1/X+4+8=0

We multiply all the terms by the denominator


X*X+4*X+8*X-1=0

We add all the numbers together, and all the variables

12X+X*X-1=0

Wy multiply elements

X^2+12X-1=0

a = 1; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·1·(-1)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{37}}{2*1}=\frac{-12-2\sqrt{37}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{37}}{2*1}=\frac{-12+2\sqrt{37}}{2}
$