3x+8=12/2x

Solution for 3x+8=12/2x equation:

3x+8=12/2x

We move all terms to the left:

3x+8-(12/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+12/2x)+8=0

We get rid of parentheses

3x-12/2x+8=0

We multiply all the terms by the denominator


3x*2x+8*2x-12=0

Wy multiply elements

6x^2+16x-12=0

a = 6; b = 16; c = -12;
Δ = b2-4ac
Δ = 162-4·6·(-12)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{34}}{2*6}=\frac{-16-4\sqrt{34}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{34}}{2*6}=\frac{-16+4\sqrt{34}}{12}
$