6=-16t^2+1250

Solution for 6=-16t^2+1250 equation:

6=-16t^2+1250

We move all terms to the left:

6-(-16t^2+1250)=0

We get rid of parentheses

16t^2-1250+6=0

We add all the numbers together, and all the variables

16t^2-1244=0

a = 16; b = 0; c = -1244;
Δ = b2-4ac
Δ = 02-4·16·(-1244)
Δ = 79616
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:

$\sqrt{\Delta}=\sqrt{79616}=\sqrt{256*311}=\sqrt{256}*\sqrt{311}=16\sqrt{311}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{311}}{2*16}=\frac{0-16\sqrt{311}}{32}
=-\frac{16\sqrt{311}}{32}
=-\frac{\sqrt{311}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{311}}{2*16}=\frac{0+16\sqrt{311}}{32}
=\frac{16\sqrt{311}}{32}
=\frac{\sqrt{311}}{2}
$