11k^2-9k-4=-5

Solution for 11k^2-9k-4=-5 equation:

11k^2-9k-4=-5

We move all terms to the left:

11k^2-9k-4-(-5)=0

We add all the numbers together, and all the variables

11k^2-9k+1=0

a = 11; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·11·1
Δ = 37
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{-(-9)-\sqrt{37}}{2*11}=\frac{9-\sqrt{37}}{22}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{37}}{2*11}=\frac{9+\sqrt{37}}{22}
$