4k^2-12k-11=0

Solution for 4k^2-12k-11=0 equation:

4k^2-12k-11=0

a = 4; b = -12; c = -11;
Δ = b2-4ac
Δ = -122-4·4·(-11)
Δ = 320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{5}}{2*4}=\frac{12-8\sqrt{5}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{5}}{2*4}=\frac{12+8\sqrt{5}}{8}
$