-4p^2-24p-27=0

Solution for -4p^2-24p-27=0 equation:

-4p^2-24p-27=0

a = -4; b = -24; c = -27;
Δ = b2-4ac
Δ = -242-4·(-4)·(-27)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12}{2*-4}=\frac{12}{-8}
=-1+1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12}{2*-4}=\frac{36}{-8}
=-4+1/2
$