105=5.4t+4.9t^2

Solution for 105=5.4t+4.9t^2 equation:

105=5.4t+4.9t^2

We move all terms to the left:

105-(5.4t+4.9t^2)=0

We get rid of parentheses

-4.9t^2-5.4t+105=0

a = -4.9; b = -5.4; c = +105;
Δ = b2-4ac
Δ = -5.42-4·(-4.9)·105
Δ = 2087.16
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{-(-5.4)-\sqrt{2087.16}}{2*-4.9}=\frac{5.4-\sqrt{2087.16}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.4)+\sqrt{2087.16}}{2*-4.9}=\frac{5.4+\sqrt{2087.16}}{-9.8}
$