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

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

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

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-9x^2-18x-1=0

We add all the numbers together, and all the variables

3x^2-18x-1=0

a = 3; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·3·(-1)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{21}}{2*3}=\frac{18-4\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{21}}{2*3}=\frac{18+4\sqrt{21}}{6}
$