5t^2-4.5t-20.2=0

Solution for 5t^2-4.5t-20.2=0 equation:

5t^2-4.5t-20.2=0

a = 5; b = -4.5; c = -20.2;
Δ = b2-4ac
Δ = -4.52-4·5·(-20.2)
Δ = 424.25
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{-(-4.5)-\sqrt{424.25}}{2*5}=\frac{4.5-\sqrt{424.25}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{424.25}}{2*5}=\frac{4.5+\sqrt{424.25}}{10}
$