(2x+1)*6=34*3/x

Solution for (2x+1)*6=34*3/x equation:

(2x+1)*6=34*3/x

We move all terms to the left:

(2x+1)*6-(34*3/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+1)*6-(+34*3/x)=0

We multiply parentheses

12x-(+34*3/x)+6=0

We get rid of parentheses

12x-34*3/x+6=0

We multiply all the terms by the denominator


12x*x+6*x-34*3=0

We add all the numbers together, and all the variables

6x+12x*x-102=0

Wy multiply elements

12x^2+6x-102=0

a = 12; b = 6; c = -102;
Δ = b2-4ac
Δ = 62-4·12·(-102)
Δ = 4932
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:

$\sqrt{\Delta}=\sqrt{4932}=\sqrt{36*137}=\sqrt{36}*\sqrt{137}=6\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{137}}{2*12}=\frac{-6-6\sqrt{137}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{137}}{2*12}=\frac{-6+6\sqrt{137}}{24}
$