3x-11=34/2x

Solution for 3x-11=34/2x equation:

3x-11=34/2x

We move all terms to the left:

3x-11-(34/2x)=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-(+34/2x)-11=0

We get rid of parentheses

3x-34/2x-11=0

We multiply all the terms by the denominator


3x*2x-11*2x-34=0

Wy multiply elements

6x^2-22x-34=0

a = 6; b = -22; c = -34;
Δ = b2-4ac
Δ = -222-4·6·(-34)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-10\sqrt{13}}{2*6}=\frac{22-10\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+10\sqrt{13}}{2*6}=\frac{22+10\sqrt{13}}{12}
$