x+1/x-6=18

Solution for x+1/x-6=18 equation:

x+1/x-6=18

We move all terms to the left:

x+1/x-6-(18)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+1/x-24=0

We multiply all the terms by the denominator


x*x-24*x+1=0

We add all the numbers together, and all the variables

-24x+x*x+1=0

Wy multiply elements

x^2-24x+1=0

a = 1; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·1·1
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{143}}{2*1}=\frac{24-2\sqrt{143}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{143}}{2*1}=\frac{24+2\sqrt{143}}{2}
$