1=9t+12.5t^2

Solution for 1=9t+12.5t^2 equation:

1=9t+12.5t^2

We move all terms to the left:

1-(9t+12.5t^2)=0

We get rid of parentheses

-12.5t^2-9t+1=0

a = -12.5; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·(-12.5)·1
Δ = 131
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{131}}{2*-12.5}=\frac{9-\sqrt{131}}{-25}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{131}}{2*-12.5}=\frac{9+\sqrt{131}}{-25}
$