-16x^2+272x=1.5

Solution for -16x^2+272x=1.5 equation:

-16x^2+272x=1.5

We move all terms to the left:

-16x^2+272x-(1.5)=0

We add all the numbers together, and all the variables

-16x^2+272x-1.5=0

a = -16; b = 272; c = -1.5;
Δ = b2-4ac
Δ = 2722-4·(-16)·(-1.5)
Δ = 73888
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:

$\sqrt{\Delta}=\sqrt{73888}=\sqrt{16*4618}=\sqrt{16}*\sqrt{4618}=4\sqrt{4618}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(272)-4\sqrt{4618}}{2*-16}=\frac{-272-4\sqrt{4618}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(272)+4\sqrt{4618}}{2*-16}=\frac{-272+4\sqrt{4618}}{-32}
$