-16x^2+32x+5.5=0

Solution for -16x^2+32x+5.5=0 equation:

-16x^2+32x+5.5=0

a = -16; b = 32; c = +5.5;
Δ = b2-4ac
Δ = 322-4·(-16)·5.5
Δ = 1376
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:

$\sqrt{\Delta}=\sqrt{1376}=\sqrt{16*86}=\sqrt{16}*\sqrt{86}=4\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{86}}{2*-16}=\frac{-32-4\sqrt{86}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{86}}{2*-16}=\frac{-32+4\sqrt{86}}{-32}
$