11p^2=1+8p

Solution for 11p^2=1+8p equation:

11p^2=1+8p

We move all terms to the left:

11p^2-(1+8p)=0

We add all the numbers together, and all the variables

11p^2-(8p+1)=0

We get rid of parentheses

11p^2-8p-1=0

a = 11; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·11·(-1)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{3}}{2*11}=\frac{8-6\sqrt{3}}{22}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{3}}{2*11}=\frac{8+6\sqrt{3}}{22}
$