x(28-x)/2=96

Solution for x(28-x)/2=96 equation:

x(28-x)/2=96

We move all terms to the left:

x(28-x)/2-(96)=0

We add all the numbers together, and all the variables

x(-1x+28)/2-96=0

We multiply all the terms by the denominator


x(-1x+28)-96*2=0

We add all the numbers together, and all the variables

x(-1x+28)-192=0

We multiply parentheses

-1x^2+28x-192=0

a = -1; b = 28; c = -192;
Δ = b2-4ac
Δ = 282-4·(-1)·(-192)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4}{2*-1}=\frac{-32}{-2}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4}{2*-1}=\frac{-24}{-2}
=+12
$