-16t^2+48t=-250

Solution for -16t^2+48t=-250 equation:

-16t^2+48t=-250

We move all terms to the left:

-16t^2+48t-(-250)=0

We add all the numbers together, and all the variables

-16t^2+48t+250=0

a = -16; b = 48; c = +250;
Δ = b2-4ac
Δ = 482-4·(-16)·250
Δ = 18304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18304}=\sqrt{64*286}=\sqrt{64}*\sqrt{286}=8\sqrt{286}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{286}}{2*-16}=\frac{-48-8\sqrt{286}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{286}}{2*-16}=\frac{-48+8\sqrt{286}}{-32}
$