80k^2+k-5.25=0

Solution for 80k^2+k-5.25=0 equation:

80k^2+k-5.25=0

a = 80; b = 1; c = -5.25;
Δ = b2-4ac
Δ = 12-4·80·(-5.25)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-41}{2*80}=\frac{-42}{160}
=-21/80
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+41}{2*80}=\frac{40}{160}
=1/4
$