8p^2-12p=16

Solution for 8p^2-12p=16 equation:

8p^2-12p=16

We move all terms to the left:

8p^2-12p-(16)=0

a = 8; b = -12; c = -16;
Δ = b2-4ac
Δ = -122-4·8·(-16)
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{41}}{2*8}=\frac{12-4\sqrt{41}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{41}}{2*8}=\frac{12+4\sqrt{41}}{16}
$