4p^2-8p=20

Solution for 4p^2-8p=20 equation:

4p^2-8p=20

We move all terms to the left:

4p^2-8p-(20)=0

a = 4; b = -8; c = -20;
Δ = b2-4ac
Δ = -82-4·4·(-20)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{6}}{2*4}=\frac{8-8\sqrt{6}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{6}}{2*4}=\frac{8+8\sqrt{6}}{8}
$