T=-5t2+15t+20

Solution for T=-5t2+15t+20 equation:

=-5T^2+15T+20

We move all terms to the left:

-(-5T^2+15T+20)=0

We get rid of parentheses

5T^2-15T-20=0

a = 5; b = -15; c = -20;
Δ = b2-4ac
Δ = -152-4·5·(-20)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-25}{2*5}=\frac{-10}{10}
=-1
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+25}{2*5}=\frac{40}{10}
=4
$