3x-1/3x=32

Solution for 3x-1/3x=32 equation:

3x-1/3x=32

We move all terms to the left:

3x-1/3x-(32)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


3x*3x-32*3x-1=0

Wy multiply elements

9x^2-96x-1=0

a = 9; b = -96; c = -1;
Δ = b2-4ac
Δ = -962-4·9·(-1)
Δ = 9252
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:

$\sqrt{\Delta}=\sqrt{9252}=\sqrt{36*257}=\sqrt{36}*\sqrt{257}=6\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-6\sqrt{257}}{2*9}=\frac{96-6\sqrt{257}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+6\sqrt{257}}{2*9}=\frac{96+6\sqrt{257}}{18}
$