x+1/x-4=8

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

x+1/x-4=8

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+1/x-12=0

We multiply all the terms by the denominator


x*x-12*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 = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{35}}{2*1}=\frac{12-2\sqrt{35}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{35}}{2*1}=\frac{12+2\sqrt{35}}{2}
$