12p-9p^2=-3

Solution for 12p-9p^2=-3 equation:

12p-9p^2=-3

We move all terms to the left:

12p-9p^2-(-3)=0

We add all the numbers together, and all the variables

-9p^2+12p+3=0

a = -9; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·(-9)·3
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{7}}{2*-9}=\frac{-12-6\sqrt{7}}{-18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{7}}{2*-9}=\frac{-12+6\sqrt{7}}{-18}
$