-16x^2-52x+14=0

Solution for -16x^2-52x+14=0 equation:

-16x^2-52x+14=0

a = -16; b = -52; c = +14;
Δ = b2-4ac
Δ = -522-4·(-16)·14
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-60}{2*-16}=\frac{-8}{-32}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+60}{2*-16}=\frac{112}{-32}
=-3+1/2
$