-16x^2+128x+1.5=0

Solution for -16x^2+128x+1.5=0 equation:

-16x^2+128x+1.5=0

a = -16; b = 128; c = +1.5;
Δ = b2-4ac
Δ = 1282-4·(-16)·1.5
Δ = 16480
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:

$\sqrt{\Delta}=\sqrt{16480}=\sqrt{16*1030}=\sqrt{16}*\sqrt{1030}=4\sqrt{1030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-4\sqrt{1030}}{2*-16}=\frac{-128-4\sqrt{1030}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+4\sqrt{1030}}{2*-16}=\frac{-128+4\sqrt{1030}}{-32}
$