4x^2+3x=12

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Solution for 4x^2+3x=12 equation:


Simplifying
4x2 + 3x = 12

Reorder the terms:
3x + 4x2 = 12

Solving
3x + 4x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 3x + 4x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 3x + 4x2 = 0

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

Divide each side by '4'.
-3 + 0.75x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 0.75x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 0.75x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 0.75x + x2 = 0 + 3
0.75x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
0.75x + x2 = 3

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 3 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 3 + 0.140625

Combine like terms: 3 + 0.140625 = 3.140625
0.140625 + 0.75x + x2 = 3.140625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 3.140625

Calculate the square root of the right side: 1.77218086

Break this problem into two subproblems by setting 
(x + 0.375) equal to 1.77218086 and -1.77218086.

Subproblem 1

x + 0.375 = 1.77218086 Simplifying x + 0.375 = 1.77218086 Reorder the terms: 0.375 + x = 1.77218086 Solving 0.375 + x = 1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 1.77218086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.77218086 + -0.375 x = 1.77218086 + -0.375 Combine like terms: 1.77218086 + -0.375 = 1.39718086 x = 1.39718086 Simplifying x = 1.39718086

Subproblem 2

x + 0.375 = -1.77218086 Simplifying x + 0.375 = -1.77218086 Reorder the terms: 0.375 + x = -1.77218086 Solving 0.375 + x = -1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -1.77218086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.77218086 + -0.375 x = -1.77218086 + -0.375 Combine like terms: -1.77218086 + -0.375 = -2.14718086 x = -2.14718086 Simplifying x = -2.14718086

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.39718086, -2.14718086}

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