-16x^2+32x-1.5=0

Solution for -16x^2+32x-1.5=0 equation:

-16x^2+32x-1.5=0

a = -16; b = 32; c = -1.5;
Δ = b2-4ac
Δ = 322-4·(-16)·(-1.5)
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{58}}{2*-16}=\frac{-32-4\sqrt{58}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{58}}{2*-16}=\frac{-32+4\sqrt{58}}{-32}
$