0=2p^2-105p+192

Solution for 0=2p^2-105p+192 equation:

0=2p^2-105p+192

We move all terms to the left:

0-(2p^2-105p+192)=0

We add all the numbers together, and all the variables

-(2p^2-105p+192)=0

We get rid of parentheses

-2p^2+105p-192=0

a = -2; b = 105; c = -192;
Δ = b2-4ac
Δ = 1052-4·(-2)·(-192)
Δ = 9489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-\sqrt{9489}}{2*-2}=\frac{-105-\sqrt{9489}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{9489}}{2*-2}=\frac{-105+\sqrt{9489}}{-4}
$