5t^2=2+15t

Solution for 5t^2=2+15t equation:

Simplifying
5t2 = 2 + 15t

Solving
5t2 = 2 + 15t

Solving for variable 't'.

Reorder the terms:
-2 + -15t + 5t2 = 2 + 15t + -2 + -15t

Reorder the terms:
-2 + -15t + 5t2 = 2 + -2 + 15t + -15t

Combine like terms: 2 + -2 = 0
-2 + -15t + 5t2 = 0 + 15t + -15t
-2 + -15t + 5t2 = 15t + -15t

Combine like terms: 15t + -15t = 0
-2 + -15t + 5t2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-0.4 + -3t + t2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -3t + 0.4 + t2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -3t + t2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -3t + t2 = 0 + 0.4
-3t + t2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-3t + t2 = 0.4

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 0.4 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 0.4 + 2.25

Combine like terms: 0.4 + 2.25 = 2.65
2.25 + -3t + t2 = 2.65

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 2.65

Calculate the square root of the right side: 1.62788206

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1.62788206 and -1.62788206.

Subproblem 1
t + -1.5 = 1.62788206

Simplifying
t + -1.5 = 1.62788206

Reorder the terms:
-1.5 + t = 1.62788206

Solving
-1.5 + t = 1.62788206

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 1.62788206 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1.62788206 + 1.5
t = 1.62788206 + 1.5

Combine like terms: 1.62788206 + 1.5 = 3.12788206
t = 3.12788206

Simplifying
t = 3.12788206

Subproblem 2
t + -1.5 = -1.62788206

Simplifying
t + -1.5 = -1.62788206

Reorder the terms:
-1.5 + t = -1.62788206

Solving
-1.5 + t = -1.62788206

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -1.62788206 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1.62788206 + 1.5
t = -1.62788206 + 1.5

Combine like terms: -1.62788206 + 1.5 = -0.12788206
t = -0.12788206

Simplifying
t = -0.12788206

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.12788206, -0.12788206}