1=2t+12.5t^2

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

1=2t+12.5t^2

We move all terms to the left:

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

We get rid of parentheses

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

a = -12.5; b = -2; c = +1;
Δ = b2-4ac
Δ = -22-4·(-12.5)·1
Δ = 54
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:

$\sqrt{\Delta}=\sqrt{54}=\sqrt{9*6}=\sqrt{9}*\sqrt{6}=3\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-3\sqrt{6}}{2*-12.5}=\frac{2-3\sqrt{6}}{-25}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+3\sqrt{6}}{2*-12.5}=\frac{2+3\sqrt{6}}{-25}
$