2p^2=51+11p

Solution for 2p^2=51+11p equation:

2p^2=51+11p

We move all terms to the left:

2p^2-(51+11p)=0

We add all the numbers together, and all the variables

2p^2-(11p+51)=0

We get rid of parentheses

2p^2-11p-51=0

a = 2; b = -11; c = -51;
Δ = b2-4ac
Δ = -112-4·2·(-51)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-23}{2*2}=\frac{-12}{4}
=-3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+23}{2*2}=\frac{34}{4}
=8+1/2
$