3x-1/3x=14

Solution for 3x-1/3x=14 equation:

3x-1/3x=14

We move all terms to the left:

3x-1/3x-(14)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-14*3x-1=0

Wy multiply elements

9x^2-42x-1=0

a = 9; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·9·(-1)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-30\sqrt{2}}{2*9}=\frac{42-30\sqrt{2}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+30\sqrt{2}}{2*9}=\frac{42+30\sqrt{2}}{18}
$