1/3x=8x-4

Solution for 1/3x=8x-4 equation:

1/3x=8x-4

We move all terms to the left:

1/3x-(8x-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-8x+4=0

We multiply all the terms by the denominator


-8x*3x+4*3x+1=0

Wy multiply elements

-24x^2+12x+1=0

a = -24; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-24)·1
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*-24}=\frac{-12-4\sqrt{15}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*-24}=\frac{-12+4\sqrt{15}}{-48}
$