x+5/x=8

Solution for x+5/x=8 equation:

x+5/x=8

We move all terms to the left:

x+5/x-(8)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-8*x+5=0

We add all the numbers together, and all the variables

-8x+x*x+5=0

Wy multiply elements

x^2-8x+5=0

a = 1; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·1·5
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{11}}{2*1}=\frac{8-2\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{11}}{2*1}=\frac{8+2\sqrt{11}}{2}
$