4.9t^2-34t-180=0

Solution for 4.9t^2-34t-180=0 equation:

4.9t^2-34t-180=0

a = 4.9; b = -34; c = -180;
Δ = b2-4ac
Δ = -342-4·4.9·(-180)
Δ = 4684
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4684}=\sqrt{4*1171}=\sqrt{4}*\sqrt{1171}=2\sqrt{1171}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{1171}}{2*4.9}=\frac{34-2\sqrt{1171}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{1171}}{2*4.9}=\frac{34+2\sqrt{1171}}{9.8}
$