2p(3p-8)=14

Solution for 2p(3p-8)=14 equation:

2p(3p-8)=14

We move all terms to the left:

2p(3p-8)-(14)=0

We multiply parentheses

6p^2-16p-14=0

a = 6; b = -16; c = -14;
Δ = b2-4ac
Δ = -162-4·6·(-14)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{37}}{2*6}=\frac{16-4\sqrt{37}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{37}}{2*6}=\frac{16+4\sqrt{37}}{12}
$