7p^2-8p-5=0

Solution for 7p^2-8p-5=0 equation:

7p^2-8p-5=0

a = 7; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·7·(-5)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{51}}{2*7}=\frac{8-2\sqrt{51}}{14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{51}}{2*7}=\frac{8+2\sqrt{51}}{14}
$