2x=21/x+11

Solution for 2x=21/x+11 equation:

2x=21/x+11

We move all terms to the left:

2x-(21/x+11)=0


Domain of the equation: x+11)!=0

x∈R


We get rid of parentheses

2x-21/x-11=0

We multiply all the terms by the denominator


2x*x-11*x-21=0

We add all the numbers together, and all the variables

-11x+2x*x-21=0

Wy multiply elements

2x^2-11x-21=0

a = 2; b = -11; c = -21;
Δ = b2-4ac
Δ = -112-4·2·(-21)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*2}=\frac{28}{4}
=7
$