4(-p^2+p+5)=8

Solution for 4(-p^2+p+5)=8 equation:

4(-p^2+p+5)=8

We move all terms to the left:

4(-p^2+p+5)-(8)=0

We multiply parentheses

-4p^2+4p+20-8=0

We add all the numbers together, and all the variables

-4p^2+4p+12=0

a = -4; b = 4; c = +12;
Δ = b2-4ac
Δ = 42-4·(-4)·12
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{13}}{2*-4}=\frac{-4-4\sqrt{13}}{-8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{13}}{2*-4}=\frac{-4+4\sqrt{13}}{-8}
$