2(x+4)=6/x

Solution for 2(x+4)=6/x equation:

2(x+4)=6/x

We move all terms to the left:

2(x+4)-(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

2(x+4)-(+6/x)=0

We multiply parentheses

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 = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*2}=\frac{-8-4\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*2}=\frac{-8+4\sqrt{7}}{4}
$