1/3x=2x+8

Solution for 1/3x=2x+8 equation:

1/3x=2x+8

We move all terms to the left:

1/3x-(2x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-2x-8=0

We multiply all the terms by the denominator


-2x*3x-8*3x+1=0

Wy multiply elements

-6x^2-24x+1=0

a = -6; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·(-6)·1
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-10\sqrt{6}}{2*-6}=\frac{24-10\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+10\sqrt{6}}{2*-6}=\frac{24+10\sqrt{6}}{-12}
$