25000=2p^2=+400p

Solution for 25000=2p^2=+400p equation:

25000=2p^2=+400p

We move all terms to the left:

25000-(2p^2)=0

a = -2; b = 0; c = +25000;
Δ = b2-4ac
Δ = 02-4·(-2)·25000
Δ = 200000
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:

$\sqrt{\Delta}=\sqrt{200000}=\sqrt{40000*5}=\sqrt{40000}*\sqrt{5}=200\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{5}}{2*-2}=\frac{0-200\sqrt{5}}{-4}
=-\frac{200\sqrt{5}}{-4}
=-\frac{50\sqrt{5}}{-1}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{5}}{2*-2}=\frac{0+200\sqrt{5}}{-4}
=\frac{200\sqrt{5}}{-4}
=\frac{50\sqrt{5}}{-1}
$