2p^2-2p-89=0

Solution for 2p^2-2p-89=0 equation:

2p^2-2p-89=0

a = 2; b = -2; c = -89;
Δ = b2-4ac
Δ = -22-4·2·(-89)
Δ = 716
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:

$\sqrt{\Delta}=\sqrt{716}=\sqrt{4*179}=\sqrt{4}*\sqrt{179}=2\sqrt{179}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{179}}{2*2}=\frac{2-2\sqrt{179}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{179}}{2*2}=\frac{2+2\sqrt{179}}{4}
$