7x^2=3x+2

Solution for 7x^2=3x+2 equation:

Simplifying
7x2 = 3x + 2

Reorder the terms:
7x2 = 2 + 3x

Solving
7x2 = 2 + 3x

Solving for variable 'x'.

Reorder the terms:
-2 + -3x + 7x2 = 2 + 3x + -2 + -3x

Reorder the terms:
-2 + -3x + 7x2 = 2 + -2 + 3x + -3x

Combine like terms: 2 + -2 = 0
-2 + -3x + 7x2 = 0 + 3x + -3x
-2 + -3x + 7x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-2 + -3x + 7x2 = 0

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

Divide each side by '7'.
-0.2857142857 + -0.4285714286x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -0.4285714286x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -0.4285714286x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -0.4285714286x + x2 = 0 + 0.2857142857
-0.4285714286x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-0.4285714286x + x2 = 0.2857142857

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 = 0.2857142857 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286x + x2 = 0.2857142857 + 0.04591836735

Combine like terms: 0.2857142857 + 0.04591836735 = 0.33163265305
0.04591836735 + -0.4285714286x + x2 = 0.33163265305

Factor a perfect square on the left side:
(x + -0.2142857143)(x + -0.2142857143) = 0.33163265305

Calculate the square root of the right side: 0.575875553

Break this problem into two subproblems by setting 
(x + -0.2142857143) equal to 0.575875553 and -0.575875553.

Subproblem 1
x + -0.2142857143 = 0.575875553

Simplifying
x + -0.2142857143 = 0.575875553

Reorder the terms:
-0.2142857143 + x = 0.575875553

Solving
-0.2142857143 + x = 0.575875553

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 = 0.575875553 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = 0.575875553 + 0.2142857143
x = 0.575875553 + 0.2142857143

Combine like terms: 0.575875553 + 0.2142857143 = 0.7901612673
x = 0.7901612673

Simplifying
x = 0.7901612673

Subproblem 2
x + -0.2142857143 = -0.575875553

Simplifying
x + -0.2142857143 = -0.575875553

Reorder the terms:
-0.2142857143 + x = -0.575875553

Solving
-0.2142857143 + x = -0.575875553

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 = -0.575875553 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = -0.575875553 + 0.2142857143
x = -0.575875553 + 0.2142857143

Combine like terms: -0.575875553 + 0.2142857143 = -0.3615898387
x = -0.3615898387

Simplifying
x = -0.3615898387

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7901612673, -0.3615898387}