2x+1/x-8=x-22

Solution for 2x+1/x-8=x-22 equation:

2x+1/x-8=x-22

We move all terms to the left:

2x+1/x-8-(x-22)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2x+1/x-x+22-8=0

We multiply all the terms by the denominator


2x*x-x*x+22*x-8*x+1=0

We add all the numbers together, and all the variables

14x+2x*x-x*x+1=0

Wy multiply elements

2x^2-1x^2+14x+1=0

We add all the numbers together, and all the variables

x^2+14x+1=0

a = 1; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·1·1
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-8\sqrt{3}}{2*1}=\frac{-14-8\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+8\sqrt{3}}{2*1}=\frac{-14+8\sqrt{3}}{2}
$