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1/3x+0.2x=16

We move all terms to the left:

1/3x+0.2x-(16)=0

Domain of the equation: 3x!=0We add all the numbers together, and all the variables

x!=0/3

x!=0

x∈R

0.2x+1/3x-16=0

We multiply all the terms by the denominator

(0.2x)*3x-16*3x+1=0

We add all the numbers together, and all the variables

(+0.2x)*3x-16*3x+1=0

We multiply parentheses

0x^2-16*3x+1=0

Wy multiply elements

0x^2-48x+1=0

We add all the numbers together, and all the variables

x^2-48x+1=0

a = 1; b = -48; c = +1;

Δ = b^{2}-4ac

Δ = -48^{2}-4·1·1

Δ = 2300

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}$

The end solution:

$\sqrt{\Delta}=\sqrt{2300}=\sqrt{100*23}=\sqrt{100}*\sqrt{23}=10\sqrt{23}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-10\sqrt{23}}{2*1}=\frac{48-10\sqrt{23}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+10\sqrt{23}}{2*1}=\frac{48+10\sqrt{23}}{2} $

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