6(x)=2x(4-3x)

Solution for 6(x)=2x(4-3x) equation:

6(x)=2x(4-3x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

2x(-3x+4)

We multiply parentheses

-6x^2+8x

Back to the equation:

-(-6x^2+8x)


We get rid of parentheses

6x^2-8x+6x=0

We add all the numbers together, and all the variables

6x^2-2x=0

a = 6; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·6·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*6}=\frac{4}{12}
=1/3
$