4.9t^2-14.3t-1=0

Solution for 4.9t^2-14.3t-1=0 equation:

4.9t^2-14.3t-1=0

a = 4.9; b = -14.3; c = -1;
Δ = b2-4ac
Δ = -14.32-4·4.9·(-1)
Δ = 224.09
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{-(-14.3)-\sqrt{224.09}}{2*4.9}=\frac{14.3-\sqrt{224.09}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14.3)+\sqrt{224.09}}{2*4.9}=\frac{14.3+\sqrt{224.09}}{9.8}
$