4t^2+15t-9=0

Solution for 4t^2+15t-9=0 equation:

Simplifying
4t2 + 15t + -9 = 0

Reorder the terms:
-9 + 15t + 4t2 = 0

Solving
-9 + 15t + 4t2 = 0

Solving for variable 't'.

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

Divide each side by '4'.
-2.25 + 3.75t + t2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 3.75t + 2.25 + t2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 3.75t + t2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 3.75t + t2 = 0 + 2.25
3.75t + t2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
3.75t + t2 = 2.25

The t term is 3.75t.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75t + 3.515625 + t2 = 2.25 + 3.515625

Reorder the terms:
3.515625 + 3.75t + t2 = 2.25 + 3.515625

Combine like terms: 2.25 + 3.515625 = 5.765625
3.515625 + 3.75t + t2 = 5.765625

Factor a perfect square on the left side:
(t + 1.875)(t + 1.875) = 5.765625

Calculate the square root of the right side: 2.401171589

Break this problem into two subproblems by setting 
(t + 1.875) equal to 2.401171589 and -2.401171589.

Subproblem 1
t + 1.875 = 2.401171589

Simplifying
t + 1.875 = 2.401171589

Reorder the terms:
1.875 + t = 2.401171589

Solving
1.875 + t = 2.401171589

Solving for variable 't'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + t = 2.401171589 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + t = 2.401171589 + -1.875
t = 2.401171589 + -1.875

Combine like terms: 2.401171589 + -1.875 = 0.526171589
t = 0.526171589

Simplifying
t = 0.526171589

Subproblem 2
t + 1.875 = -2.401171589

Simplifying
t + 1.875 = -2.401171589

Reorder the terms:
1.875 + t = -2.401171589

Solving
1.875 + t = -2.401171589

Solving for variable 't'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + t = -2.401171589 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + t = -2.401171589 + -1.875
t = -2.401171589 + -1.875

Combine like terms: -2.401171589 + -1.875 = -4.276171589
t = -4.276171589

Simplifying
t = -4.276171589

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.526171589, -4.276171589}