62.5=2.5t+1.1t^2

Solution for 62.5=2.5t+1.1t^2 equation:

62.5=2.5t+1.1t^2

We move all terms to the left:

62.5-(2.5t+1.1t^2)=0

We get rid of parentheses

-1.1t^2-2.5t+62.5=0

a = -1.1; b = -2.5; c = +62.5;
Δ = b2-4ac
Δ = -2.52-4·(-1.1)·62.5
Δ = 281.25
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{-(-2.5)-\sqrt{281.25}}{2*-1.1}=\frac{2.5-\sqrt{281.25}}{-2.2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{281.25}}{2*-1.1}=\frac{2.5+\sqrt{281.25}}{-2.2}
$