16t^2-84=180

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

16t^2-84=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

16t^2-264=0

a = 16; b = 0; c = -264;
Δ = b2-4ac
Δ = 02-4·16·(-264)
Δ = 16896
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:

$\sqrt{\Delta}=\sqrt{16896}=\sqrt{256*66}=\sqrt{256}*\sqrt{66}=16\sqrt{66}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{66}}{2*16}=\frac{0-16\sqrt{66}}{32}
=-\frac{16\sqrt{66}}{32}
=-\frac{\sqrt{66}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{66}}{2*16}=\frac{0+16\sqrt{66}}{32}
=\frac{16\sqrt{66}}{32}
=\frac{\sqrt{66}}{2}
$