4.5t+4.9t^2=60.185

Solution for 4.5t+4.9t^2=60.185 equation:

4.5t+4.9t^2=60.185

We move all terms to the left:

4.5t+4.9t^2-(60.185)=0

We add all the numbers together, and all the variables

4.9t^2+4.5t-60.185=0

a = 4.9; b = 4.5; c = -60.185;
Δ = b2-4ac
Δ = 4.52-4·4.9·(-60.185)
Δ = 1199.876
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{-(4.5)-\sqrt{1199.876}}{2*4.9}=\frac{-4.5-\sqrt{1199.876}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{1199.876}}{2*4.9}=\frac{-4.5+\sqrt{1199.876}}{9.8}
$