10k^2+6k-1=0

Solution for 10k^2+6k-1=0 equation:

10k^2+6k-1=0

a = 10; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·10·(-1)
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{19}}{2*10}=\frac{-6-2\sqrt{19}}{20}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{19}}{2*10}=\frac{-6+2\sqrt{19}}{20}
$