384=x(x-4)

Solution for 384=x(x-4) equation:

384=x(x-4)

We move all terms to the left:

384-(x(x-4))=0


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

x(x-4)

We multiply parentheses

x^2-4x

Back to the equation:

-(x^2-4x)


We get rid of parentheses

-x^2+4x+384=0

We add all the numbers together, and all the variables

-1x^2+4x+384=0

a = -1; b = 4; c = +384;
Δ = b2-4ac
Δ = 42-4·(-1)·384
Δ = 1552
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:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{97}}{2*-1}=\frac{-4-4\sqrt{97}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{97}}{2*-1}=\frac{-4+4\sqrt{97}}{-2}
$