125=5.2t+4.9t^2

Solution for 125=5.2t+4.9t^2 equation:

125=5.2t+4.9t^2

We move all terms to the left:

125-(5.2t+4.9t^2)=0

We get rid of parentheses

-4.9t^2-5.2t+125=0

a = -4.9; b = -5.2; c = +125;
Δ = b2-4ac
Δ = -5.22-4·(-4.9)·125
Δ = 2477.04
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{-(-5.2)-\sqrt{2477.04}}{2*-4.9}=\frac{5.2-\sqrt{2477.04}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.2)+\sqrt{2477.04}}{2*-4.9}=\frac{5.2+\sqrt{2477.04}}{-9.8}
$