4.905t^2+5t=15

Solution for 4.905t^2+5t=15 equation:

Simplifying
4.905t2 + 5t = 15

Reorder the terms:
5t + 4.905t2 = 15

Solving
5t + 4.905t2 = 15

Solving for variable 't'.

Reorder the terms:
-15 + 5t + 4.905t2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 5t + 4.905t2 = 0

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

Divide each side by '4.905'.
-3.058103976 + 1.019367992t + t2 = 0

Move the constant term to the right:

Add '3.058103976' to each side of the equation.
-3.058103976 + 1.019367992t + 3.058103976 + t2 = 0 + 3.058103976

Reorder the terms:
-3.058103976 + 3.058103976 + 1.019367992t + t2 = 0 + 3.058103976

Combine like terms: -3.058103976 + 3.058103976 = 0.000000000
0.000000000 + 1.019367992t + t2 = 0 + 3.058103976
1.019367992t + t2 = 0 + 3.058103976

Combine like terms: 0 + 3.058103976 = 3.058103976
1.019367992t + t2 = 3.058103976

The t term is 1.019367992t.  Take half its coefficient (0.509683996).
Square it (0.2597777758) and add it to both sides.

Add '0.2597777758' to each side of the equation.
1.019367992t + 0.2597777758 + t2 = 3.058103976 + 0.2597777758

Reorder the terms:
0.2597777758 + 1.019367992t + t2 = 3.058103976 + 0.2597777758

Combine like terms: 3.058103976 + 0.2597777758 = 3.3178817518
0.2597777758 + 1.019367992t + t2 = 3.3178817518

Factor a perfect square on the left side:
(t + 0.509683996)(t + 0.509683996) = 3.3178817518

Calculate the square root of the right side: 1.821505353

Break this problem into two subproblems by setting 
(t + 0.509683996) equal to 1.821505353 and -1.821505353.

Subproblem 1
t + 0.509683996 = 1.821505353

Simplifying
t + 0.509683996 = 1.821505353

Reorder the terms:
0.509683996 + t = 1.821505353

Solving
0.509683996 + t = 1.821505353

Solving for variable 't'.

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

Add '-0.509683996' to each side of the equation.
0.509683996 + -0.509683996 + t = 1.821505353 + -0.509683996

Combine like terms: 0.509683996 + -0.509683996 = 0.000000000
0.000000000 + t = 1.821505353 + -0.509683996
t = 1.821505353 + -0.509683996

Combine like terms: 1.821505353 + -0.509683996 = 1.311821357
t = 1.311821357

Simplifying
t = 1.311821357

Subproblem 2
t + 0.509683996 = -1.821505353

Simplifying
t + 0.509683996 = -1.821505353

Reorder the terms:
0.509683996 + t = -1.821505353

Solving
0.509683996 + t = -1.821505353

Solving for variable 't'.

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

Add '-0.509683996' to each side of the equation.
0.509683996 + -0.509683996 + t = -1.821505353 + -0.509683996

Combine like terms: 0.509683996 + -0.509683996 = 0.000000000
0.000000000 + t = -1.821505353 + -0.509683996
t = -1.821505353 + -0.509683996

Combine like terms: -1.821505353 + -0.509683996 = -2.331189349
t = -2.331189349

Simplifying
t = -2.331189349

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.311821357, -2.331189349}