3x^2+24x-7=0

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Solution for 3x^2+24x-7=0 equation: 


Simplifying
3x2 + 24x + -7 = 0

Reorder the terms:
-7 + 24x + 3x2 = 0

Solving
-7 + 24x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-2.333333333 + 8x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 8x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 8x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 8x + x2 = 0 + 2.333333333
8x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
8x + x2 = 2.333333333

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 2.333333333 + 16

Reorder the terms:
16 + 8x + x2 = 2.333333333 + 16

Combine like terms: 2.333333333 + 16 = 18.333333333
16 + 8x + x2 = 18.333333333

Factor a perfect square on the left side:
(x + 4)(x + 4) = 18.333333333

Calculate the square root of the right side: 4.281744193

Break this problem into two subproblems by setting 
(x + 4) equal to 4.281744193 and -4.281744193.


Subproblem 1
x + 4 = 4.281744193

Simplifying
x + 4 = 4.281744193

Reorder the terms:
4 + x = 4.281744193

Solving
4 + x = 4.281744193

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.281744193 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.281744193 + -4
x = 4.281744193 + -4

Combine like terms: 4.281744193 + -4 = 0.281744193
x = 0.281744193

Simplifying
x = 0.281744193


Subproblem 2
x + 4 = -4.281744193

Simplifying
x + 4 = -4.281744193

Reorder the terms:
4 + x = -4.281744193

Solving
4 + x = -4.281744193

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.281744193 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.281744193 + -4
x = -4.281744193 + -4

Combine like terms: -4.281744193 + -4 = -8.281744193
x = -8.281744193

Simplifying
x = -8.281744193


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.281744193, -8.281744193}

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