4x=3(2+x)4x=3(2+x)

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

4x=3(2+x)4x=3(2+x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(3(x+2)4x), so:

3(x+2)4x

We multiply parentheses

12x^2+24x

Back to the equation:

-(12x^2+24x)


We get rid of parentheses

-12x^2+4x-24x=0

We add all the numbers together, and all the variables

-12x^2-20x=0

a = -12; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-12)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-12}=\frac{40}{-24}
=-1+2/3
$