0=-16t2+130t-3

Solution for 0=-16t2+130t-3 equation:

0=-16t^2+130t-3

We move all terms to the left:

0-(-16t^2+130t-3)=0

We add all the numbers together, and all the variables

-(-16t^2+130t-3)=0

We get rid of parentheses

16t^2-130t+3=0

a = 16; b = -130; c = +3;
Δ = b2-4ac
Δ = -1302-4·16·3
Δ = 16708
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:

$\sqrt{\Delta}=\sqrt{16708}=\sqrt{4*4177}=\sqrt{4}*\sqrt{4177}=2\sqrt{4177}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4177}}{2*16}=\frac{130-2\sqrt{4177}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4177}}{2*16}=\frac{130+2\sqrt{4177}}{32}
$