x(1+5/x)=8

Solution for x(1+5/x)=8 equation:

x(1+5/x)=8

We move all terms to the left:

x(1+5/x)-(8)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x(5/x+1)-8=0

We multiply parentheses

5x^2+x-8=0

a = 5; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·5·(-8)
Δ = 161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{161}}{2*5}=\frac{-1-\sqrt{161}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{161}}{2*5}=\frac{-1+\sqrt{161}}{10}
$