What is the solution for 75 = -5t^2 + 40t

We'll use the symmetric property for the given expression and
we'll get:

5t^2 - 40t = -75

We'll
divide by 5 all over:

t^2 - 8t =
-15

Now, we'll have to complete the square from the left side. For
this purpose, we'll add both sides the number 16:

t^2 - 8t + 16 = 16
- 15

We'll recognize the
square:

(t-4)^2 = 1

We'll consider 2
cases:

1) t - 4 = sqrt 1

t - 4 = 1
=> t = 5

2) t - 4 = -sqrt 1

t -
4 = -1 => t = 3

There are 2 solutions for the equation above
(since it's order is 2) and they are: {3 ; 5}.