3+9p=6p^2

Solution for 3+9p=6p^2 equation:

3+9p=6p^2

We move all terms to the left:

3+9p-(6p^2)=0

determiningTheFunctionDomain
-6p^2+9p+3=0

a = -6; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·(-6)·3
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{17}}{2*-6}=\frac{-9-3\sqrt{17}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{17}}{2*-6}=\frac{-9+3\sqrt{17}}{-12}
$