12p-8p^2=-2

Solution for 12p-8p^2=-2 equation:

12p-8p^2=-2

We move all terms to the left:

12p-8p^2-(-2)=0

We add all the numbers together, and all the variables

-8p^2+12p+2=0

a = -8; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·(-8)·2
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{13}}{2*-8}=\frac{-12-4\sqrt{13}}{-16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{13}}{2*-8}=\frac{-12+4\sqrt{13}}{-16}
$