4p^2-84=16p

Solution for 4p^2-84=16p equation:

4p^2-84=16p

We move all terms to the left:

4p^2-84-(16p)=0

a = 4; b = -16; c = -84;
Δ = b2-4ac
Δ = -162-4·4·(-84)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-40}{2*4}=\frac{-24}{8}
=-3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+40}{2*4}=\frac{56}{8}
=7
$