8p^2-22p+5=0

Solution for 8p^2-22p+5=0 equation:

8p^2-22p+5=0

a = 8; b = -22; c = +5;
Δ = b2-4ac
Δ = -222-4·8·5
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-18}{2*8}=\frac{4}{16}
=1/4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+18}{2*8}=\frac{40}{16}
=2+1/2
$