480-30t^2=400

Solution for 480-30t^2=400 equation:

480-30t^2=400

We move all terms to the left:

480-30t^2-(400)=0

We add all the numbers together, and all the variables

-30t^2+80=0

a = -30; b = 0; c = +80;
Δ = b2-4ac
Δ = 02-4·(-30)·80
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*-30}=\frac{0-40\sqrt{6}}{-60}
=-\frac{40\sqrt{6}}{-60}
=-\frac{2\sqrt{6}}{-3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*-30}=\frac{0+40\sqrt{6}}{-60}
=\frac{40\sqrt{6}}{-60}
=\frac{2\sqrt{6}}{-3}
$