12=4x(4-x)

Solution for 12=4x(4-x) equation:

12=4x(4-x)

We move all terms to the left:

12-(4x(4-x))=0

We add all the numbers together, and all the variables

-(4x(-1x+4))+12=0


We calculate terms in parentheses: -(4x(-1x+4)), so:

4x(-1x+4)

We multiply parentheses

-4x^2+16x

Back to the equation:

-(-4x^2+16x)


We get rid of parentheses

4x^2-16x+12=0

a = 4; b = -16; c = +12;
Δ = b2-4ac
Δ = -162-4·4·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*4}=\frac{24}{8}
=3
$