p^2+2p=0.5

Solution for p^2+2p=0.5 equation:

p^2+2p=0.5

We move all terms to the left:

p^2+2p-(0.5)=0

We add all the numbers together, and all the variables

p^2+2p-0.5=0

a = 1; b = 2; c = -0.5;
Δ = b2-4ac
Δ = 22-4·1·(-0.5)
Δ = 6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-\sqrt{6}}{2*1}=\frac{-2-\sqrt{6}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{6}}{2*1}=\frac{-2+\sqrt{6}}{2}
$