9p=-7p^2-1

Solution for 9p=-7p^2-1 equation:

9p=-7p^2-1

We move all terms to the left:

9p-(-7p^2-1)=0

We get rid of parentheses

7p^2+9p+1=0

a = 7; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·7·1
Δ = 53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{53}}{2*7}=\frac{-9-\sqrt{53}}{14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{53}}{2*7}=\frac{-9+\sqrt{53}}{14}
$