2x+x+1/3x=16.9

Solution for 2x+x+1/3x=16.9 equation:

2x+x+1/3x=16.9

We move all terms to the left:

2x+x+1/3x-(16.9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/3x-16.9=0

We multiply all the terms by the denominator


3x*3x-(16.9)*3x+1=0

We multiply parentheses

3x*3x-50.7x+1=0

Wy multiply elements

9x^2-50.7x+1=0

a = 9; b = -50.7; c = +1;
Δ = b2-4ac
Δ = -50.72-4·9·1
Δ = 2534.49
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{-(-50.7)-\sqrt{2534.49}}{2*9}=\frac{50.7-\sqrt{2534.49}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50.7)+\sqrt{2534.49}}{2*9}=\frac{50.7+\sqrt{2534.49}}{18}
$