p^2+2p(0.3)+0.09=1

Solution for p^2+2p(0.3)+0.09=1 equation:

p^2+2p(0.3)+0.09=1

We move all terms to the left:

p^2+2p(0.3)+0.09-(1)=0

We add all the numbers together, and all the variables

p^2+2p(0.3)-0.91=0

We multiply parentheses

p^2+0.6p-0.91=0

a = 1; b = 0.6; c = -0.91;
Δ = b2-4ac
Δ = 0.62-4·1·(-0.91)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.6)-2}{2*1}=\frac{-2.6}{2}
=-1+0.6/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.6)+2}{2*1}=\frac{1.4}{2}
=1/1.4285714285714
$