9p^2+12p+4=8

Solution for 9p^2+12p+4=8 equation:

9p^2+12p+4=8

We move all terms to the left:

9p^2+12p+4-(8)=0

We add all the numbers together, and all the variables

9p^2+12p-4=0

a = 9; b = 12; c = -4;
Δ = b2-4ac
Δ = 122-4·9·(-4)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{2}}{2*9}=\frac{-12-12\sqrt{2}}{18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{2}}{2*9}=\frac{-12+12\sqrt{2}}{18}
$