7k^2-6k-8=0

Solution for 7k^2-6k-8=0 equation:

7k^2-6k-8=0

a = 7; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·7·(-8)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{65}}{2*7}=\frac{6-2\sqrt{65}}{14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{65}}{2*7}=\frac{6+2\sqrt{65}}{14}
$