k(k+5)=11

Solution for k(k+5)=11 equation:

k(k+5)=11

We move all terms to the left:

k(k+5)-(11)=0

We multiply parentheses

k^2+5k-11=0

a = 1; b = 5; c = -11;
Δ = b2-4ac
Δ = 52-4·1·(-11)
Δ = 69
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{-(5)-\sqrt{69}}{2*1}=\frac{-5-\sqrt{69}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{69}}{2*1}=\frac{-5+\sqrt{69}}{2}
$