1/3x+3x=19

Solution for 1/3x+3x=19 equation:

1/3x+3x=19

We move all terms to the left:

1/3x+3x-(19)=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-19=0

We multiply all the terms by the denominator


3x*3x-19*3x+1=0

Wy multiply elements

9x^2-57x+1=0

a = 9; b = -57; c = +1;
Δ = b2-4ac
Δ = -572-4·9·1
Δ = 3213
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:

$\sqrt{\Delta}=\sqrt{3213}=\sqrt{9*357}=\sqrt{9}*\sqrt{357}=3\sqrt{357}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-3\sqrt{357}}{2*9}=\frac{57-3\sqrt{357}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+3\sqrt{357}}{2*9}=\frac{57+3\sqrt{357}}{18}
$