-p+8p2=16

Solution for -p+8p2=16 equation:

-p+8p^2=16

We move all terms to the left:

-p+8p^2-(16)=0

We add all the numbers together, and all the variables

8p^2-1p-16=0

a = 8; b = -1; c = -16;
Δ = b2-4ac
Δ = -12-4·8·(-16)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{57}}{2*8}=\frac{1-3\sqrt{57}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{57}}{2*8}=\frac{1+3\sqrt{57}}{16}
$