-2p^2+8p+5=0

Solution for -2p^2+8p+5=0 equation:

-2p^2+8p+5=0

a = -2; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·(-2)·5
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{26}}{2*-2}=\frac{-8-2\sqrt{26}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{26}}{2*-2}=\frac{-8+2\sqrt{26}}{-4}
$