7k^2-6k-17=0

Solution for 7k^2-6k-17=0 equation:

7k^2-6k-17=0

a = 7; b = -6; c = -17;
Δ = b2-4ac
Δ = -62-4·7·(-17)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-16\sqrt{2}}{2*7}=\frac{6-16\sqrt{2}}{14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+16\sqrt{2}}{2*7}=\frac{6+16\sqrt{2}}{14}
$