12p+1=9p^2

Solution for 12p+1=9p^2 equation:

12p+1=9p^2

We move all terms to the left:

12p+1-(9p^2)=0

determiningTheFunctionDomain
-9p^2+12p+1=0

a = -9; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-9)·1
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{5}}{2*-9}=\frac{-12-6\sqrt{5}}{-18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{5}}{2*-9}=\frac{-12+6\sqrt{5}}{-18}
$