76-21p=2p-p^2

Solution for 76-21p=2p-p^2 equation:

76-21p=2p-p^2

We move all terms to the left:

76-21p-(2p-p^2)=0

We get rid of parentheses

p^2-2p-21p+76=0

We add all the numbers together, and all the variables

p^2-23p+76=0

a = 1; b = -23; c = +76;
Δ = b2-4ac
Δ = -232-4·1·76
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-15}{2*1}=\frac{8}{2}
=4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+15}{2*1}=\frac{38}{2}
=19
$