t(4.9t+24.5)=0

Solution for t(4.9t+24.5)=0 equation:

t(4.9t+24.5)=0

We multiply parentheses

4t^2+24.5t=0

a = 4; b = 24.5; c = 0;
Δ = b2-4ac
Δ = 24.52-4·4·0
Δ = 600.25
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{-(24.5)-\sqrt{600.25}}{2*4}=\frac{-24.5-\sqrt{600.25}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24.5)+\sqrt{600.25}}{2*4}=\frac{-24.5+\sqrt{600.25}}{8}
$