4k(k+16)=14

Solution for 4k(k+16)=14 equation:

4k(k+16)=14

We move all terms to the left:

4k(k+16)-(14)=0

We multiply parentheses

4k^2+64k-14=0

a = 4; b = 64; c = -14;
Δ = b2-4ac
Δ = 642-4·4·(-14)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-12\sqrt{30}}{2*4}=\frac{-64-12\sqrt{30}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+12\sqrt{30}}{2*4}=\frac{-64+12\sqrt{30}}{8}
$