180-16t^2=84

Solution for 180-16t^2=84 equation:

180-16t^2=84

We move all terms to the left:

180-16t^2-(84)=0

We add all the numbers together, and all the variables

-16t^2+96=0

a = -16; b = 0; c = +96;
Δ = b2-4ac
Δ = 02-4·(-16)·96
Δ = 6144
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:

$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{6}}{2*-16}=\frac{0-32\sqrt{6}}{-32}
=-\frac{32\sqrt{6}}{-32}
=-\frac{\sqrt{6}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{6}}{2*-16}=\frac{0+32\sqrt{6}}{-32}
=\frac{32\sqrt{6}}{-32}
=\frac{\sqrt{6}}{-1}
$