10=(0)t+(0.5)(3.71)t^2

Solution for 10=(0)t+(0.5)(3.71)t^2 equation:

Simplifying
10 = (0) * t + (0.5)(3.71) * t2

Anything times zero is zero.
10 = 0t + (0.5)(3.71) * t2

Multiply 0.5 * 3.71
10 = 0 + 1.855t2
Remove the zero:
10 = 1.855t2

Solving
10 = 1.855t2

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-1.855t2' to each side of the equation.
10 + -1.855t2 = 1.855t2 + -1.855t2

Combine like terms: 1.855t2 + -1.855t2 = 0.000
10 + -1.855t2 = 0.000

Add '-10' to each side of the equation.
10 + -10 + -1.855t2 = 0.000 + -10

Combine like terms: 10 + -10 = 0
0 + -1.855t2 = 0.000 + -10
-1.855t2 = 0.000 + -10

Combine like terms: 0.000 + -10 = -10
-1.855t2 = -10

Divide each side by '-1.855'.
t2 = 5.39083558

Simplifying
t2 = 5.39083558

Take the square root of each side:
t = {-2.321817301, 2.321817301}