1250=100t+16t^2

Solution for 1250=100t+16t^2 equation:

1250=100t+16t^2

We move all terms to the left:

1250-(100t+16t^2)=0

We get rid of parentheses

-16t^2-100t+1250=0

a = -16; b = -100; c = +1250;
Δ = b2-4ac
Δ = -1002-4·(-16)·1250
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-300}{2*-16}=\frac{-200}{-32}
=6+1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+300}{2*-16}=\frac{400}{-32}
=-12+1/2
$