5x^2+19x-7=0

Solution for 5x^2+19x-7=0 equation:

Simplifying
5x2 + 19x + -7 = 0

Reorder the terms:
-7 + 19x + 5x2 = 0

Solving
-7 + 19x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1.4 + 3.8x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 3.8x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 3.8x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 3.8x + x2 = 0 + 1.4
3.8x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
3.8x + x2 = 1.4

The x term is 3.8x.  Take half its coefficient (1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
3.8x + 3.61 + x2 = 1.4 + 3.61

Reorder the terms:
3.61 + 3.8x + x2 = 1.4 + 3.61

Combine like terms: 1.4 + 3.61 = 5.01
3.61 + 3.8x + x2 = 5.01

Factor a perfect square on the left side:
(x + 1.9)(x + 1.9) = 5.01

Calculate the square root of the right side: 2.238302929

Break this problem into two subproblems by setting 
(x + 1.9) equal to 2.238302929 and -2.238302929.

Subproblem 1
x + 1.9 = 2.238302929

Simplifying
x + 1.9 = 2.238302929

Reorder the terms:
1.9 + x = 2.238302929

Solving
1.9 + x = 2.238302929

Solving for variable 'x'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + x = 2.238302929 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = 2.238302929 + -1.9
x = 2.238302929 + -1.9

Combine like terms: 2.238302929 + -1.9 = 0.338302929
x = 0.338302929

Simplifying
x = 0.338302929

Subproblem 2
x + 1.9 = -2.238302929

Simplifying
x + 1.9 = -2.238302929

Reorder the terms:
1.9 + x = -2.238302929

Solving
1.9 + x = -2.238302929

Solving for variable 'x'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + x = -2.238302929 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = -2.238302929 + -1.9
x = -2.238302929 + -1.9

Combine like terms: -2.238302929 + -1.9 = -4.138302929
x = -4.138302929

Simplifying
x = -4.138302929

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.338302929, -4.138302929}