5p^2-24p-27=0

Solution for 5p^2-24p-27=0 equation:

5p^2-24p-27=0

a = 5; b = -24; c = -27;
Δ = b2-4ac
Δ = -242-4·5·(-27)
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{31}}{2*5}=\frac{24-6\sqrt{31}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{31}}{2*5}=\frac{24+6\sqrt{31}}{10}
$