-0.3+1.5p-1.5p^2=0.05

Solution for -0.3+1.5p-1.5p^2=0.05 equation:

-0.3+1.5p-1.5p^2=0.05

We move all terms to the left:

-0.3+1.5p-1.5p^2-(0.05)=0

We add all the numbers together, and all the variables

-1.5p^2+1.5p-0.35=0

a = -1.5; b = 1.5; c = -0.35;
Δ = b2-4ac
Δ = 1.52-4·(-1.5)·(-0.35)
Δ = 0.15
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{-(1.5)-\sqrt{0.15}}{2*-1.5}=\frac{-1.5-\sqrt{0.15}}{-3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{0.15}}{2*-1.5}=\frac{-1.5+\sqrt{0.15}}{-3}
$