4x(-4x-14)=14

Solution for 4x(-4x-14)=14 equation:

4x(-4x-14)=14

We move all terms to the left:

4x(-4x-14)-(14)=0

We multiply parentheses

-16x^2-56x-14=0

a = -16; b = -56; c = -14;
Δ = b2-4ac
Δ = -562-4·(-16)·(-14)
Δ = 2240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{35}}{2*-16}=\frac{56-8\sqrt{35}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{35}}{2*-16}=\frac{56+8\sqrt{35}}{-32}
$