2p^2-105=11p

Solution for 2p^2-105=11p equation:

2p^2-105=11p

We move all terms to the left:

2p^2-105-(11p)=0

a = 2; b = -11; c = -105;
Δ = b2-4ac
Δ = -112-4·2·(-105)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-31}{2*2}=\frac{-20}{4}
=-5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+31}{2*2}=\frac{42}{4}
=10+1/2
$