0=-7x^2+3x+5

Solution for 0=-7x^2+3x+5 equation:

Simplifying
0 = -7x2 + 3x + 5

Reorder the terms:
0 = 5 + 3x + -7x2

Solving
0 = 5 + 3x + -7x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -3x + 7x2 = 5 + 3x + -7x2 + -5 + -3x + 7x2

Reorder the terms:
-5 + -3x + 7x2 = 5 + -5 + 3x + -3x + -7x2 + 7x2

Combine like terms: 5 + -5 = 0
-5 + -3x + 7x2 = 0 + 3x + -3x + -7x2 + 7x2
-5 + -3x + 7x2 = 3x + -3x + -7x2 + 7x2

Combine like terms: 3x + -3x = 0
-5 + -3x + 7x2 = 0 + -7x2 + 7x2
-5 + -3x + 7x2 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
-5 + -3x + 7x2 = 0

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

Divide each side by '7'.
-0.7142857143 + -0.4285714286x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + -0.4285714286x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + -0.4285714286x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + -0.4285714286x + x2 = 0 + 0.7142857143
-0.4285714286x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
-0.4285714286x + x2 = 0.7142857143

The x term is -0.4285714286x.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286x + 0.04591836735 + x2 = 0.7142857143 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286x + x2 = 0.7142857143 + 0.04591836735

Combine like terms: 0.7142857143 + 0.04591836735 = 0.76020408165
0.04591836735 + -0.4285714286x + x2 = 0.76020408165

Factor a perfect square on the left side:
(x + -0.2142857143)(x + -0.2142857143) = 0.76020408165

Calculate the square root of the right side: 0.87189683

Break this problem into two subproblems by setting 
(x + -0.2142857143) equal to 0.87189683 and -0.87189683.

Subproblem 1
x + -0.2142857143 = 0.87189683

Simplifying
x + -0.2142857143 = 0.87189683

Reorder the terms:
-0.2142857143 + x = 0.87189683

Solving
-0.2142857143 + x = 0.87189683

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = 0.87189683 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = 0.87189683 + 0.2142857143
x = 0.87189683 + 0.2142857143

Combine like terms: 0.87189683 + 0.2142857143 = 1.0861825443
x = 1.0861825443

Simplifying
x = 1.0861825443

Subproblem 2
x + -0.2142857143 = -0.87189683

Simplifying
x + -0.2142857143 = -0.87189683

Reorder the terms:
-0.2142857143 + x = -0.87189683

Solving
-0.2142857143 + x = -0.87189683

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = -0.87189683 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = -0.87189683 + 0.2142857143
x = -0.87189683 + 0.2142857143

Combine like terms: -0.87189683 + 0.2142857143 = -0.6576111157
x = -0.6576111157

Simplifying
x = -0.6576111157

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0861825443, -0.6576111157}