7x^2+3x-5=0

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


Simplifying
7x2 + 3x + -5 = 0

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

Solving
-5 + 3x + 7x2 = 0

Solving for variable 'x'.

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 = 0.6576111157
x = 0.6576111157

Simplifying
x = 0.6576111157


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 = -1.0861825443
x = -1.0861825443

Simplifying
x = -1.0861825443


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

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