3n^2+4n-24=0

Simple and best practice solution for 3n^2+4n-24=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 3n^2+4n-24=0 equation: 


Simplifying
3n2 + 4n + -24 = 0

Reorder the terms:
-24 + 4n + 3n2 = 0

Solving
-24 + 4n + 3n2 = 0

Solving for variable 'n'.

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

Divide each side by '3'.
-8 + 1.333333333n + n2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 1.333333333n + 8 + n2 = 0 + 8

Reorder the terms:
-8 + 8 + 1.333333333n + n2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 1.333333333n + n2 = 0 + 8
1.333333333n + n2 = 0 + 8

Combine like terms: 0 + 8 = 8
1.333333333n + n2 = 8

The n term is 1.333333333n.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333n + 0.4444444442 + n2 = 8 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333n + n2 = 8 + 0.4444444442

Combine like terms: 8 + 0.4444444442 = 8.4444444442
0.4444444442 + 1.333333333n + n2 = 8.4444444442

Factor a perfect square on the left side:
(n + 0.6666666665)(n + 0.6666666665) = 8.4444444442

Calculate the square root of the right side: 2.905932629

Break this problem into two subproblems by setting 
(n + 0.6666666665) equal to 2.905932629 and -2.905932629.


Subproblem 1
n + 0.6666666665 = 2.905932629

Simplifying
n + 0.6666666665 = 2.905932629

Reorder the terms:
0.6666666665 + n = 2.905932629

Solving
0.6666666665 + n = 2.905932629

Solving for variable 'n'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + n = 2.905932629 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + n = 2.905932629 + -0.6666666665
n = 2.905932629 + -0.6666666665

Combine like terms: 2.905932629 + -0.6666666665 = 2.2392659625
n = 2.2392659625

Simplifying
n = 2.2392659625


Subproblem 2
n + 0.6666666665 = -2.905932629

Simplifying
n + 0.6666666665 = -2.905932629

Reorder the terms:
0.6666666665 + n = -2.905932629

Solving
0.6666666665 + n = -2.905932629

Solving for variable 'n'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + n = -2.905932629 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + n = -2.905932629 + -0.6666666665
n = -2.905932629 + -0.6666666665

Combine like terms: -2.905932629 + -0.6666666665 = -3.5725992955
n = -3.5725992955

Simplifying
n = -3.5725992955


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.2392659625, -3.5725992955}

See similar equations:

| 7x+4x=154 | | x^4+4x^2=45 | | 1x=6x-6x+3 | | -(3v-u)+(-6u-6v)= | | 8x+12y=4 | | 15x-10= | | 5(6x-9)=15 | | 8+5-9= | | 0.09=0.6+1.1x+4.44 | | 9x+5=2x-4 | | x^3-x^2y-6xy^2= | | 3n-3(6n-8)=-15-2n | | -9x^2+36x=43 | | 6x+18y=42 | | -9abc-9ac^2+3bc+3c^2= | | 15(3x-2)-12(4x-1)=-14(2x+5) | | 4(x-12)=10x-16-5x | | 0.2(4-x)+0.3x=0.7x+0.9 | | x^4-x^3-x^2+2x-2=0 | | -4x^2+8x-7= | | x=-x+5 | | 9x+9=89 | | 2.3x-1.2=1.8x+0.4 | | 3(y+7)=5-3y | | (3k+1)-(4-k)= | | 2x+7=5x-13 | | 5y-7=20 | | 152-4x=23x+20 | | 16x=64 | | 3(3+4x)-2=67 | | 4+x=6+x^2 | | 5x-7y+7a= |

Equations solver categories