0=16t^2+5t-74

Solution for 0=16t^2+5t-74 equation:

0=16t^2+5t-74

We move all terms to the left:

0-(16t^2+5t-74)=0

We add all the numbers together, and all the variables

-(16t^2+5t-74)=0

We get rid of parentheses

-16t^2-5t+74=0

a = -16; b = -5; c = +74;
Δ = b2-4ac
Δ = -52-4·(-16)·74
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-69}{2*-16}=\frac{-64}{-32}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+69}{2*-16}=\frac{74}{-32}
=-2+5/16
$