x(-16x-39)=14

Solution for x(-16x-39)=14 equation:

x(-16x-39)=14

We move all terms to the left:

x(-16x-39)-(14)=0

We multiply parentheses

-16x^2-39x-14=0

a = -16; b = -39; c = -14;
Δ = b2-4ac
Δ = -392-4·(-16)·(-14)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-25}{2*-16}=\frac{14}{-32}
=-7/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+25}{2*-16}=\frac{64}{-32}
=-2
$