432=x(96-2x)/2

Solution for 432=x(96-2x)/2 equation:

432=x(96-2x)/2

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(x(-2x+96)/2)+432=0

We multiply all the terms by the denominator


-(x(-2x+96)+432*2)=0


We calculate terms in parentheses: -(x(-2x+96)+432*2), so:

x(-2x+96)+432*2

We add all the numbers together, and all the variables

x(-2x+96)+864

We multiply parentheses

-2x^2+96x+864

Back to the equation:

-(-2x^2+96x+864)


We get rid of parentheses

2x^2-96x-864=0

a = 2; b = -96; c = -864;
Δ = b2-4ac
Δ = -962-4·2·(-864)
Δ = 16128
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:

$\sqrt{\Delta}=\sqrt{16128}=\sqrt{2304*7}=\sqrt{2304}*\sqrt{7}=48\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-48\sqrt{7}}{2*2}=\frac{96-48\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+48\sqrt{7}}{2*2}=\frac{96+48\sqrt{7}}{4}
$