4.9t^2-10.1t-75=0

Solution for 4.9t^2-10.1t-75=0 equation:

4.9t^2-10.1t-75=0

a = 4.9; b = -10.1; c = -75;
Δ = b2-4ac
Δ = -10.12-4·4.9·(-75)
Δ = 1572.01
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{-(-10.1)-\sqrt{1572.01}}{2*4.9}=\frac{10.1-\sqrt{1572.01}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10.1)+\sqrt{1572.01}}{2*4.9}=\frac{10.1+\sqrt{1572.01}}{9.8}
$