12=4x(9-x)

Solution for 12=4x(9-x) equation:

12=4x(9-x)

We move all terms to the left:

12-(4x(9-x))=0

We add all the numbers together, and all the variables

-(4x(-1x+9))+12=0


We calculate terms in parentheses: -(4x(-1x+9)), so:

4x(-1x+9)

We multiply parentheses

-4x^2+36x

Back to the equation:

-(-4x^2+36x)


We get rid of parentheses

4x^2-36x+12=0

a = 4; b = -36; c = +12;
Δ = b2-4ac
Δ = -362-4·4·12
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{69}}{2*4}=\frac{36-4\sqrt{69}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{69}}{2*4}=\frac{36+4\sqrt{69}}{8}
$