7=3x^2-7x

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


Simplifying
7 = 3x2 + -7x

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

Solving
7 = -7x + 3x2

Solving for variable 'x'.

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

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

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

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-2.333333333 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -2.333333333x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -2.333333333x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + 2.333333333
-2.333333333x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-2.333333333x + x2 = 2.333333333

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 2.333333333 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 2.333333333 + 1.361111112

Combine like terms: 2.333333333 + 1.361111112 = 3.694444445
1.361111112 + -2.333333333x + x2 = 3.694444445

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 3.694444445

Calculate the square root of the right side: 1.922093766

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 1.922093766 and -1.922093766.


Subproblem 1
x + -1.166666667 = 1.922093766

Simplifying
x + -1.166666667 = 1.922093766

Reorder the terms:
-1.166666667 + x = 1.922093766

Solving
-1.166666667 + x = 1.922093766

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 1.922093766 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 1.922093766 + 1.166666667
x = 1.922093766 + 1.166666667

Combine like terms: 1.922093766 + 1.166666667 = 3.088760433
x = 3.088760433

Simplifying
x = 3.088760433


Subproblem 2
x + -1.166666667 = -1.922093766

Simplifying
x + -1.166666667 = -1.922093766

Reorder the terms:
-1.166666667 + x = -1.922093766

Solving
-1.166666667 + x = -1.922093766

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -1.922093766 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -1.922093766 + 1.166666667
x = -1.922093766 + 1.166666667

Combine like terms: -1.922093766 + 1.166666667 = -0.755427099
x = -0.755427099

Simplifying
x = -0.755427099


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.088760433, -0.755427099}

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