2x=11+6/x

Solution for 2x=11+6/x equation:

2x=11+6/x

We move all terms to the left:

2x-(11+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

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

We get rid of parentheses

2x-6/x-11=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2-11x-6=0

a = 2; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·2·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-13}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+13}{2*2}=\frac{24}{4}
=6
$