1/3x-4=2x+6

Solution for 1/3x-4=2x+6 equation:

1/3x-4=2x+6

We move all terms to the left:

1/3x-4-(2x+6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-2x-6-4=0

We multiply all the terms by the denominator


-2x*3x-6*3x-4*3x+1=0

Wy multiply elements

-6x^2-18x-12x+1=0

We add all the numbers together, and all the variables

-6x^2-30x+1=0

a = -6; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·(-6)·1
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{231}}{2*-6}=\frac{30-2\sqrt{231}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{231}}{2*-6}=\frac{30+2\sqrt{231}}{-12}
$