1+2k-8k^2=0

Solution for 1+2k-8k^2=0 equation:

1+2k-8k^2=0

a = -8; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-8)·1
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*-8}=\frac{-8}{-16}
=1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*-8}=\frac{4}{-16}
=-1/4
$