4p2-8p-19=0

Solution for 4p2-8p-19=0 equation:

4p^2-8p-19=0

a = 4; b = -8; c = -19;
Δ = b2-4ac
Δ = -82-4·4·(-19)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{23}}{2*4}=\frac{8-4\sqrt{23}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{23}}{2*4}=\frac{8+4\sqrt{23}}{8}
$