16k^2-4(-2k^2+11k-4)=0

Solution for 16k^2-4(-2k^2+11k-4)=0 equation:

16k^2-4(-2k^2+11k-4)=0

We multiply parentheses

16k^2+8k^2-44k+16=0

We add all the numbers together, and all the variables

24k^2-44k+16=0

a = 24; b = -44; c = +16;
Δ = b2-4ac
Δ = -442-4·24·16
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-20}{2*24}=\frac{24}{48}
=1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+20}{2*24}=\frac{64}{48}
=1+1/3
$