4(k-2)k=5

Solution for 4(k-2)k=5 equation:

4(k-2)k=5

We move all terms to the left:

4(k-2)k-(5)=0

We multiply parentheses

4k^2-8k-5=0

a = 4; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·4·(-5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*4}=\frac{-4}{8}
=-1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*4}=\frac{20}{8}
=2+1/2
$