84p=720-294p^2

Solution for 84p=720-294p^2 equation:

84p=720-294p^2

We move all terms to the left:

84p-(720-294p^2)=0

We get rid of parentheses

294p^2+84p-720=0

a = 294; b = 84; c = -720;
Δ = b2-4ac
Δ = 842-4·294·(-720)
Δ = 853776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{853776}=924$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-924}{2*294}=\frac{-1008}{588}
=-1+5/7
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+924}{2*294}=\frac{840}{588}
=1+3/7
$