-16t^2-45t^2+200=0

Solution for -16t^2-45t^2+200=0 equation:

-16t^2-45t^2+200=0

We add all the numbers together, and all the variables

-61t^2+200=0

a = -61; b = 0; c = +200;
Δ = b2-4ac
Δ = 02-4·(-61)·200
Δ = 48800
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:

$\sqrt{\Delta}=\sqrt{48800}=\sqrt{400*122}=\sqrt{400}*\sqrt{122}=20\sqrt{122}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{122}}{2*-61}=\frac{0-20\sqrt{122}}{-122}
=-\frac{20\sqrt{122}}{-122}
=-\frac{10\sqrt{122}}{-61}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{122}}{2*-61}=\frac{0+20\sqrt{122}}{-122}
=\frac{20\sqrt{122}}{-122}
=\frac{10\sqrt{122}}{-61}
$