7k^2-7k=1

Solution for 7k^2-7k=1 equation:

7k^2-7k=1

We move all terms to the left:

7k^2-7k-(1)=0

a = 7; b = -7; c = -1;
Δ = b2-4ac
Δ = -72-4·7·(-1)
Δ = 77
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{77}}{2*7}=\frac{7-\sqrt{77}}{14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{77}}{2*7}=\frac{7+\sqrt{77}}{14}
$