11p^2-17p-20=p

Solution for 11p^2-17p-20=p equation:

11p^2-17p-20=p

We move all terms to the left:

11p^2-17p-20-(p)=0

We add all the numbers together, and all the variables

11p^2-18p-20=0

a = 11; b = -18; c = -20;
Δ = b2-4ac
Δ = -182-4·11·(-20)
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{301}}{2*11}=\frac{18-2\sqrt{301}}{22}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{301}}{2*11}=\frac{18+2\sqrt{301}}{22}
$