2k(-2+8k)=14

Solution for 2k(-2+8k)=14 equation:

2k(-2+8k)=14

We move all terms to the left:

2k(-2+8k)-(14)=0

We add all the numbers together, and all the variables

2k(8k-2)-14=0

We multiply parentheses

16k^2-4k-14=0

a = 16; b = -4; c = -14;
Δ = b2-4ac
Δ = -42-4·16·(-14)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{57}}{2*16}=\frac{4-4\sqrt{57}}{32}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{57}}{2*16}=\frac{4+4\sqrt{57}}{32}
$