6x-11=17/2x

Solution for 6x-11=17/2x equation:

6x-11=17/2x

We move all terms to the left:

6x-11-(17/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+17/2x)-11=0

We get rid of parentheses

6x-17/2x-11=0

We multiply all the terms by the denominator


6x*2x-11*2x-17=0

Wy multiply elements

12x^2-22x-17=0

a = 12; b = -22; c = -17;
Δ = b2-4ac
Δ = -222-4·12·(-17)
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*12}=\frac{22-10\sqrt{13}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+10\sqrt{13}}{2*12}=\frac{22+10\sqrt{13}}{24}
$