5t^2+3t-30=0

Solution for 5t^2+3t-30=0 equation:

Simplifying
5t2 + 3t + -30 = 0

Reorder the terms:
-30 + 3t + 5t2 = 0

Solving
-30 + 3t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
-6 + 0.6t + t2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 0.6t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + 0.6t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 0.6t + t2 = 0 + 6
0.6t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
0.6t + t2 = 6

The t term is 0.6t.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6t + 0.09 + t2 = 6 + 0.09

Reorder the terms:
0.09 + 0.6t + t2 = 6 + 0.09

Combine like terms: 6 + 0.09 = 6.09
0.09 + 0.6t + t2 = 6.09

Factor a perfect square on the left side:
(t + 0.3)(t + 0.3) = 6.09

Calculate the square root of the right side: 2.467792536

Break this problem into two subproblems by setting 
(t + 0.3) equal to 2.467792536 and -2.467792536.

Subproblem 1
t + 0.3 = 2.467792536

Simplifying
t + 0.3 = 2.467792536

Reorder the terms:
0.3 + t = 2.467792536

Solving
0.3 + t = 2.467792536

Solving for variable 't'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + t = 2.467792536 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + t = 2.467792536 + -0.3
t = 2.467792536 + -0.3

Combine like terms: 2.467792536 + -0.3 = 2.167792536
t = 2.167792536

Simplifying
t = 2.167792536

Subproblem 2
t + 0.3 = -2.467792536

Simplifying
t + 0.3 = -2.467792536

Reorder the terms:
0.3 + t = -2.467792536

Solving
0.3 + t = -2.467792536

Solving for variable 't'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + t = -2.467792536 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + t = -2.467792536 + -0.3
t = -2.467792536 + -0.3

Combine like terms: -2.467792536 + -0.3 = -2.767792536
t = -2.767792536

Simplifying
t = -2.767792536

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.167792536, -2.767792536}