k^2=11k-30

Solution for k^2=11k-30 equation:

k^2=11k-30

We move all terms to the left:

k^2-(11k-30)=0

We get rid of parentheses

k^2-11k+30=0

a = 1; b = -11; c = +30;
Δ = b2-4ac
Δ = -112-4·1·30
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-1}{2*1}=\frac{10}{2}
=5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*1}=\frac{12}{2}
=6
$