240t=-16t^2+1200

Solution for 240t=-16t^2+1200 equation:

240t=-16t^2+1200

We move all terms to the left:

240t-(-16t^2+1200)=0

We get rid of parentheses

16t^2+240t-1200=0

a = 16; b = 240; c = -1200;
Δ = b2-4ac
Δ = 2402-4·16·(-1200)
Δ = 134400
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:

$\sqrt{\Delta}=\sqrt{134400}=\sqrt{6400*21}=\sqrt{6400}*\sqrt{21}=80\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-80\sqrt{21}}{2*16}=\frac{-240-80\sqrt{21}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+80\sqrt{21}}{2*16}=\frac{-240+80\sqrt{21}}{32}
$