0=24-1/2p^2

Solution for 0=24-1/2p^2 equation:

0=24-1/2p^2

We move all terms to the left:

0-(24-1/2p^2)=0


Domain of the equation: 2p^2)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

-(24-1/2p^2)=0

We get rid of parentheses

1/2p^2-24=0

We multiply all the terms by the denominator


-24*2p^2+1=0

Wy multiply elements

-48p^2+1=0

a = -48; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-48)·1
Δ = 192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-48}=\frac{0-8\sqrt{3}}{-96}
=-\frac{8\sqrt{3}}{-96}
=-\frac{\sqrt{3}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-48}=\frac{0+8\sqrt{3}}{-96}
=\frac{8\sqrt{3}}{-96}
=\frac{\sqrt{3}}{-12}
$