3p=3-8p^2

Solution for 3p=3-8p^2 equation:

3p=3-8p^2

We move all terms to the left:

3p-(3-8p^2)=0

We get rid of parentheses

8p^2+3p-3=0

a = 8; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·8·(-3)
Δ = 105
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{-(3)-\sqrt{105}}{2*8}=\frac{-3-\sqrt{105}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*8}=\frac{-3+\sqrt{105}}{16}
$