3x-1/3x=16

Solution for 3x-1/3x=16 equation:

3x-1/3x=16

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-16*3x-1=0

Wy multiply elements

9x^2-48x-1=0

a = 9; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·9·(-1)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-6\sqrt{65}}{2*9}=\frac{48-6\sqrt{65}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+6\sqrt{65}}{2*9}=\frac{48+6\sqrt{65}}{18}
$