5.25=25t+2.5t^2

Solution for 5.25=25t+2.5t^2 equation:

5.25=25t+2.5t^2

We move all terms to the left:

5.25-(25t+2.5t^2)=0

We get rid of parentheses

-2.5t^2-25t+5.25=0

a = -2.5; b = -25; c = +5.25;
Δ = b2-4ac
Δ = -252-4·(-2.5)·5.25
Δ = 677.5
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{-(-25)-\sqrt{677.5}}{2*-2.5}=\frac{25-\sqrt{677.5}}{-5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{677.5}}{2*-2.5}=\frac{25+\sqrt{677.5}}{-5}
$