1/3x-8=4x+2

Solution for 1/3x-8=4x+2 equation:

1/3x-8=4x+2

We move all terms to the left:

1/3x-8-(4x+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-4x-2-8=0

We multiply all the terms by the denominator


-4x*3x-2*3x-8*3x+1=0

Wy multiply elements

-12x^2-6x-24x+1=0

We add all the numbers together, and all the variables

-12x^2-30x+1=0

a = -12; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·(-12)·1
Δ = 948
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:

$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{237}}{2*-12}=\frac{30-2\sqrt{237}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{237}}{2*-12}=\frac{30+2\sqrt{237}}{-24}
$