-4.9x^2+26x+2.4=0

Solution for -4.9x^2+26x+2.4=0 equation:

Simplifying
-4.9x2 + 26x + 2.4 = 0

Reorder the terms:
2.4 + 26x + -4.9x2 = 0

Solving
2.4 + 26x + -4.9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-0.4897959184 + -5.306122449x + x2 = 0

Move the constant term to the right:

Add '0.4897959184' to each side of the equation.
-0.4897959184 + -5.306122449x + 0.4897959184 + x2 = 0 + 0.4897959184

Reorder the terms:
-0.4897959184 + 0.4897959184 + -5.306122449x + x2 = 0 + 0.4897959184

Combine like terms: -0.4897959184 + 0.4897959184 = 0.0000000000
0.0000000000 + -5.306122449x + x2 = 0 + 0.4897959184
-5.306122449x + x2 = 0 + 0.4897959184

Combine like terms: 0 + 0.4897959184 = 0.4897959184
-5.306122449x + x2 = 0.4897959184

The x term is -5.306122449x.  Take half its coefficient (-2.653061225).
Square it (7.038733864) and add it to both sides.

Add '7.038733864' to each side of the equation.
-5.306122449x + 7.038733864 + x2 = 0.4897959184 + 7.038733864

Reorder the terms:
7.038733864 + -5.306122449x + x2 = 0.4897959184 + 7.038733864

Combine like terms: 0.4897959184 + 7.038733864 = 7.5285297824
7.038733864 + -5.306122449x + x2 = 7.5285297824

Factor a perfect square on the left side:
(x + -2.653061225)(x + -2.653061225) = 7.5285297824

Calculate the square root of the right side: 2.743816645

Break this problem into two subproblems by setting 
(x + -2.653061225) equal to 2.743816645 and -2.743816645.

Subproblem 1
x + -2.653061225 = 2.743816645

Simplifying
x + -2.653061225 = 2.743816645

Reorder the terms:
-2.653061225 + x = 2.743816645

Solving
-2.653061225 + x = 2.743816645

Solving for variable 'x'.

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

Add '2.653061225' to each side of the equation.
-2.653061225 + 2.653061225 + x = 2.743816645 + 2.653061225

Combine like terms: -2.653061225 + 2.653061225 = 0.000000000
0.000000000 + x = 2.743816645 + 2.653061225
x = 2.743816645 + 2.653061225

Combine like terms: 2.743816645 + 2.653061225 = 5.39687787
x = 5.39687787

Simplifying
x = 5.39687787

Subproblem 2
x + -2.653061225 = -2.743816645

Simplifying
x + -2.653061225 = -2.743816645

Reorder the terms:
-2.653061225 + x = -2.743816645

Solving
-2.653061225 + x = -2.743816645

Solving for variable 'x'.

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

Add '2.653061225' to each side of the equation.
-2.653061225 + 2.653061225 + x = -2.743816645 + 2.653061225

Combine like terms: -2.653061225 + 2.653061225 = 0.000000000
0.000000000 + x = -2.743816645 + 2.653061225
x = -2.743816645 + 2.653061225

Combine like terms: -2.743816645 + 2.653061225 = -0.09075542
x = -0.09075542

Simplifying
x = -0.09075542

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.39687787, -0.09075542}