-9p^2+3=2p

Solution for -9p^2+3=2p equation:

-9p^2+3=2p

We move all terms to the left:

-9p^2+3-(2p)=0

a = -9; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-9)·3
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{7}}{2*-9}=\frac{2-4\sqrt{7}}{-18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{7}}{2*-9}=\frac{2+4\sqrt{7}}{-18}
$