2x+(1/3x)=21

Solution for 2x+(1/3x)=21 equation:

2x+(1/3x)=21

We move all terms to the left:

2x+(1/3x)-(21)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+(+1/3x)-21=0

We get rid of parentheses

2x+1/3x-21=0

We multiply all the terms by the denominator


2x*3x-21*3x+1=0

Wy multiply elements

6x^2-63x+1=0

a = 6; b = -63; c = +1;
Δ = b2-4ac
Δ = -632-4·6·1
Δ = 3945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-\sqrt{3945}}{2*6}=\frac{63-\sqrt{3945}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{3945}}{2*6}=\frac{63+\sqrt{3945}}{12}
$