11k2-4k-11=4

Solution for 11k2-4k-11=4 equation:

11k^2-4k-11=4

We move all terms to the left:

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

We add all the numbers together, and all the variables

11k^2-4k-15=0

a = 11; b = -4; c = -15;
Δ = b2-4ac
Δ = -42-4·11·(-15)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-26}{2*11}=\frac{-22}{22}
=-1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+26}{2*11}=\frac{30}{22}
=1+4/11
$