9.8t^2-20.9t-12=0

Solution for 9.8t^2-20.9t-12=0 equation:

9.8t^2-20.9t-12=0

a = 9.8; b = -20.9; c = -12;
Δ = b2-4ac
Δ = -20.92-4·9.8·(-12)
Δ = 907.21
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{-(-20.9)-\sqrt{907.21}}{2*9.8}=\frac{20.9-\sqrt{907.21}}{19.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20.9)+\sqrt{907.21}}{2*9.8}=\frac{20.9+\sqrt{907.21}}{19.6}
$