11k^2-9k=4

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

11k^2-9k=4

We move all terms to the left:

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

a = 11; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·11·(-4)
Δ = 257
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{257}}{2*11}=\frac{9-\sqrt{257}}{22}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{257}}{2*11}=\frac{9+\sqrt{257}}{22}
$