3x=1/3x-8

Solution for 3x=1/3x-8 equation:

3x=1/3x-8

We move all terms to the left:

3x-(1/3x-8)=0


Domain of the equation: 3x-8)!=0

x∈R


We get rid of parentheses

3x-1/3x+8=0

We multiply all the terms by the denominator


3x*3x+8*3x-1=0

Wy multiply elements

9x^2+24x-1=0

a = 9; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·9·(-1)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{17}}{2*9}=\frac{-24-6\sqrt{17}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{17}}{2*9}=\frac{-24+6\sqrt{17}}{18}
$