40t-4.44t^2=90

Solution for 40t-4.44t^2=90 equation:

40t-4.44t^2=90

We move all terms to the left:

40t-4.44t^2-(90)=0

a = -4.44; b = 40; c = -90;
Δ = b2-4ac
Δ = 402-4·(-4.44)·(-90)
Δ = 1.5999999999999
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{-(40)-\sqrt{1.5999999999999}}{2*-4.44}=\frac{-40-\sqrt{1.5999999999999}}{-8.88}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+\sqrt{1.5999999999999}}{2*-4.44}=\frac{-40+\sqrt{1.5999999999999}}{-8.88}
$