-1-9p^2=-55

Solution for -1-9p^2=-55 equation:

-1-9p^2=-55

We move all terms to the left:

-1-9p^2-(-55)=0

We add all the numbers together, and all the variables

-9p^2+54=0

a = -9; b = 0; c = +54;
Δ = b2-4ac
Δ = 02-4·(-9)·54
Δ = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{6}}{2*-9}=\frac{0-18\sqrt{6}}{-18}
=-\frac{18\sqrt{6}}{-18}
=-\frac{\sqrt{6}}{-1}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{6}}{2*-9}=\frac{0+18\sqrt{6}}{-18}
=\frac{18\sqrt{6}}{-18}
=\frac{\sqrt{6}}{-1}
$