5.25=-16t^2+20

Solution for 5.25=-16t^2+20 equation:

5.25=-16t^2+20

We move all terms to the left:

5.25-(-16t^2+20)=0

We get rid of parentheses

16t^2-20+5.25=0

We add all the numbers together, and all the variables

16t^2-14.75=0

a = 16; b = 0; c = -14.75;
Δ = b2-4ac
Δ = 02-4·16·(-14.75)
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{59}}{2*16}=\frac{0-4\sqrt{59}}{32}
=-\frac{4\sqrt{59}}{32}
=-\frac{\sqrt{59}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{59}}{2*16}=\frac{0+4\sqrt{59}}{32}
=\frac{4\sqrt{59}}{32}
=\frac{\sqrt{59}}{8}
$