4p^2-5p-8=0

Solution for 4p^2-5p-8=0 equation:

4p^2-5p-8=0

a = 4; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·4·(-8)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{17}}{2*4}=\frac{5-3\sqrt{17}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{17}}{2*4}=\frac{5+3\sqrt{17}}{8}
$