2k2-2k-10=0

Solution for 2k2-2k-10=0 equation:

2k^2-2k-10=0

a = 2; b = -2; c = -10;
Δ = b2-4ac
Δ = -22-4·2·(-10)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{21}}{2*2}=\frac{2-2\sqrt{21}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{21}}{2*2}=\frac{2+2\sqrt{21}}{4}
$