-32t=400-16t^2

Solution for -32t=400-16t^2 equation:

-32t=400-16t^2

We move all terms to the left:

-32t-(400-16t^2)=0

We get rid of parentheses

16t^2-32t-400=0

a = 16; b = -32; c = -400;
Δ = b2-4ac
Δ = -322-4·16·(-400)
Δ = 26624
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:

$\sqrt{\Delta}=\sqrt{26624}=\sqrt{1024*26}=\sqrt{1024}*\sqrt{26}=32\sqrt{26}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32\sqrt{26}}{2*16}=\frac{32-32\sqrt{26}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32\sqrt{26}}{2*16}=\frac{32+32\sqrt{26}}{32}
$