k2-7k=7=-5

Solution for k2-7k=7=-5 equation:

k2-7k=7=-5

We move all terms to the left:

k2-7k-(7)=0

We add all the numbers together, and all the variables

k^2-7k-7=0

a = 1; b = -7; c = -7;
Δ = b2-4ac
Δ = -72-4·1·(-7)
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*1}=\frac{7-\sqrt{77}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{77}}{2*1}=\frac{7+\sqrt{77}}{2}
$