38=38-3t-5t^2

Solution for 38=38-3t-5t^2 equation:

38=38-3t-5t^2

We move all terms to the left:

38-(38-3t-5t^2)=0

We get rid of parentheses

5t^2+3t-38+38=0

We add all the numbers together, and all the variables

5t^2+3t=0

a = 5; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·5·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*5}=\frac{-6}{10}
=-3/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*5}=\frac{0}{10}
=0
$