4p^2-8p-64=7

Solution for 4p^2-8p-64=7 equation:

4p^2-8p-64=7

We move all terms to the left:

4p^2-8p-64-(7)=0

We add all the numbers together, and all the variables

4p^2-8p-71=0

a = 4; b = -8; c = -71;
Δ = b2-4ac
Δ = -82-4·4·(-71)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20\sqrt{3}}{2*4}=\frac{8-20\sqrt{3}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20\sqrt{3}}{2*4}=\frac{8+20\sqrt{3}}{8}
$