4p^2-8p-23=0

Solution for 4p^2-8p-23=0 equation:

4p^2-8p-23=0

a = 4; b = -8; c = -23;
Δ = b2-4ac
Δ = -82-4·4·(-23)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{3}}{2*4}=\frac{8-12\sqrt{3}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{3}}{2*4}=\frac{8+12\sqrt{3}}{8}
$