5x^2=3(x+1)

Solution for 5x^2=3(x+1) equation:

Simplifying
5x2 = 3(x + 1)

Reorder the terms:
5x2 = 3(1 + x)
5x2 = (1 * 3 + x * 3)
5x2 = (3 + 3x)

Solving
5x2 = 3 + 3x

Solving for variable 'x'.

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

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

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

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

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

Divide each side by '5'.
-0.6 + -0.6x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -0.6x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -0.6x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -0.6x + x2 = 0 + 0.6
-0.6x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-0.6x + x2 = 0.6

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 0.6 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 0.6 + 0.09

Combine like terms: 0.6 + 0.09 = 0.69
0.09 + -0.6x + x2 = 0.69

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 0.69

Calculate the square root of the right side: 0.830662386

Break this problem into two subproblems by setting 
(x + -0.3) equal to 0.830662386 and -0.830662386.

Subproblem 1
x + -0.3 = 0.830662386

Simplifying
x + -0.3 = 0.830662386

Reorder the terms:
-0.3 + x = 0.830662386

Solving
-0.3 + x = 0.830662386

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = 0.830662386 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 0.830662386 + 0.3
x = 0.830662386 + 0.3

Combine like terms: 0.830662386 + 0.3 = 1.130662386
x = 1.130662386

Simplifying
x = 1.130662386

Subproblem 2
x + -0.3 = -0.830662386

Simplifying
x + -0.3 = -0.830662386

Reorder the terms:
-0.3 + x = -0.830662386

Solving
-0.3 + x = -0.830662386

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = -0.830662386 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -0.830662386 + 0.3
x = -0.830662386 + 0.3

Combine like terms: -0.830662386 + 0.3 = -0.530662386
x = -0.530662386

Simplifying
x = -0.530662386

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.130662386, -0.530662386}