T=-5t^2+24t+4

Solution for T=-5t^2+24t+4 equation:

=-5T^2+24T+4

We move all terms to the left:

-(-5T^2+24T+4)=0

We get rid of parentheses

5T^2-24T-4=0

a = 5; b = -24; c = -4;
Δ = b2-4ac
Δ = -242-4·5·(-4)
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{41}}{2*5}=\frac{24-4\sqrt{41}}{10}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{41}}{2*5}=\frac{24+4\sqrt{41}}{10}
$