8=2x+6/x

Solution for 8=2x+6/x equation:

8=2x+6/x

We move all terms to the left:

8-(2x+6/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+2x+6/x)+8=0

We get rid of parentheses

-2x-6/x+8=0

We multiply all the terms by the denominator


-2x*x+8*x-6=0

We add all the numbers together, and all the variables

8x-2x*x-6=0

Wy multiply elements

-2x^2+8x-6=0

a = -2; b = 8; c = -6;
Δ = b2-4ac
Δ = 82-4·(-2)·(-6)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4}{2*-2}=\frac{-4}{-4}
=1
$