0=16t^2+38t=5

Solution for 0=16t^2+38t=5 equation:

0=16t^2+38t=5

We move all terms to the left:

0-(16t^2+38t)=0

We add all the numbers together, and all the variables

-(16t^2+38t)=0

We get rid of parentheses

-16t^2-38t=0

a = -16; b = -38; c = 0;
Δ = b2-4ac
Δ = -382-4·(-16)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-38}{2*-16}=\frac{0}{-32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+38}{2*-16}=\frac{76}{-32}
=-2+3/8
$