24t-0.8t^2=90

Solution for 24t-0.8t^2=90 equation:

24t-0.8t^2=90

We move all terms to the left:

24t-0.8t^2-(90)=0

a = -0.8; b = 24; c = -90;
Δ = b2-4ac
Δ = 242-4·(-0.8)·(-90)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{2}}{2*-0.8}=\frac{-24-12\sqrt{2}}{-1.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{2}}{2*-0.8}=\frac{-24+12\sqrt{2}}{-1.6}
$