0=-16t^2+30t-5

Solution for 0=-16t^2+30t-5 equation:

0=-16t^2+30t-5

We move all terms to the left:

0-(-16t^2+30t-5)=0

We add all the numbers together, and all the variables

-(-16t^2+30t-5)=0

We get rid of parentheses

16t^2-30t+5=0

a = 16; b = -30; c = +5;
Δ = b2-4ac
Δ = -302-4·16·5
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{145}}{2*16}=\frac{30-2\sqrt{145}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{145}}{2*16}=\frac{30+2\sqrt{145}}{32}
$