3x=121/x+2x

Solution for 3x=121/x+2x equation:

3x=121/x+2x

We move all terms to the left:

3x-(121/x+2x)=0


Domain of the equation: x+2x)!=0

x∈R


We add all the numbers together, and all the variables

3x-(+2x+121/x)=0

We get rid of parentheses

3x-2x-121/x=0

We multiply all the terms by the denominator


3x*x-2x*x-121=0

Wy multiply elements

3x^2-2x^2-121=0

We add all the numbers together, and all the variables

x^2-121=0

a = 1; b = 0; c = -121;
Δ = b2-4ac
Δ = 02-4·1·(-121)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22}{2*1}=\frac{22}{2}
=11
$