-16x^2+48x=0.25

Solution for -16x^2+48x=0.25 equation:

-16x^2+48x=0.25

We move all terms to the left:

-16x^2+48x-(0.25)=0

We add all the numbers together, and all the variables

-16x^2+48x-0.25=0

a = -16; b = 48; c = -0.25;
Δ = b2-4ac
Δ = 482-4·(-16)·(-0.25)
Δ = 2288
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:

$\sqrt{\Delta}=\sqrt{2288}=\sqrt{16*143}=\sqrt{16}*\sqrt{143}=4\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{143}}{2*-16}=\frac{-48-4\sqrt{143}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{143}}{2*-16}=\frac{-48+4\sqrt{143}}{-32}
$