96=(x-4)(x)

Solution for 96=(x-4)(x) equation:

96=(x-4)(x)

We move all terms to the left:

96-((x-4)(x))=0


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

(x-4)x

We multiply parentheses

x^2-4x

Back to the equation:

-(x^2-4x)


We get rid of parentheses

-x^2+4x+96=0

We add all the numbers together, and all the variables

-1x^2+4x+96=0

a = -1; b = 4; c = +96;
Δ = b2-4ac
Δ = 42-4·(-1)·96
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{-(4)-20}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20}{2*-1}=\frac{16}{-2}
=-8
$