x+5/x=18

Solution for x+5/x=18 equation:

x+5/x=18

We move all terms to the left:

x+5/x-(18)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-18*x+5=0

We add all the numbers together, and all the variables

-18x+x*x+5=0

Wy multiply elements

x^2-18x+5=0

a = 1; b = -18; c = +5;
Δ = b2-4ac
Δ = -182-4·1·5
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{19}}{2*1}=\frac{18-4\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{19}}{2*1}=\frac{18+4\sqrt{19}}{2}
$