4.9t^2-42.63t-12.5=0

Solution for 4.9t^2-42.63t-12.5=0 equation:

4.9t^2-42.63t-12.5=0

a = 4.9; b = -42.63; c = -12.5;
Δ = b2-4ac
Δ = -42.632-4·4.9·(-12.5)
Δ = 2062.3169
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{-(-42.63)-\sqrt{2062.3169}}{2*4.9}=\frac{42.63-\sqrt{2062.3169}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42.63)+\sqrt{2062.3169}}{2*4.9}=\frac{42.63+\sqrt{2062.3169}}{9.8}
$