3n^2+4n=9

Simple and best practice solution for 3n^2+4n=9 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=9 equation:


Simplifying
3n2 + 4n = 9

Reorder the terms:
4n + 3n2 = 9

Solving
4n + 3n2 = 9

Solving for variable 'n'.

Reorder the terms:
-9 + 4n + 3n2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 4n + 3n2 = 0

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

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

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 1.333333333n + 3 + n2 = 0 + 3

Reorder the terms:
-3 + 3 + 1.333333333n + n2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 1.333333333n + n2 = 0 + 3
1.333333333n + n2 = 0 + 3

Combine like terms: 0 + 3 = 3
1.333333333n + n2 = 3

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 = 3 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333n + n2 = 3 + 0.4444444442

Combine like terms: 3 + 0.4444444442 = 3.4444444442
0.4444444442 + 1.333333333n + n2 = 3.4444444442

Factor a perfect square on the left side:
(n + 0.6666666665)(n + 0.6666666665) = 3.4444444442

Calculate the square root of the right side: 1.855921454

Break this problem into two subproblems by setting 
(n + 0.6666666665) equal to 1.855921454 and -1.855921454.

Subproblem 1

n + 0.6666666665 = 1.855921454 Simplifying n + 0.6666666665 = 1.855921454 Reorder the terms: 0.6666666665 + n = 1.855921454 Solving 0.6666666665 + n = 1.855921454 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 = 1.855921454 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + n = 1.855921454 + -0.6666666665 n = 1.855921454 + -0.6666666665 Combine like terms: 1.855921454 + -0.6666666665 = 1.1892547875 n = 1.1892547875 Simplifying n = 1.1892547875

Subproblem 2

n + 0.6666666665 = -1.855921454 Simplifying n + 0.6666666665 = -1.855921454 Reorder the terms: 0.6666666665 + n = -1.855921454 Solving 0.6666666665 + n = -1.855921454 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 = -1.855921454 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + n = -1.855921454 + -0.6666666665 n = -1.855921454 + -0.6666666665 Combine like terms: -1.855921454 + -0.6666666665 = -2.5225881205 n = -2.5225881205 Simplifying n = -2.5225881205

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.1892547875, -2.5225881205}

See similar equations:

| x+(x-30)+3x=x | | 3x+(x+30)=x | | 6(4a-2b+5)+2(3a-6)= | | 3x+(x-30)=x | | -2x^3+9x+5=0 | | 3-(2x+3(x+2)+4)+6x+7=2x-2(x-4) | | (x*x)+x=200 | | 4x+21=7x+4 | | t^2+100t-50=0 | | x+(x+30)=3x | | (x*x)+x=170 | | 6x^2-31x+5=0 | | x+(x-30)=3x | | -16t^2+100t-50=0 | | 1=m+5 | | x-30=3x | | 14y-11y= | | (x*x)+x=210 | | 5a-19a-5a= | | 1/4+1/6= | | (x*x)+x=198 | | n-36=-49 | | k^2-12k+35=0 | | 5p+9=11+4p | | (3x^2+7)(25x^2-5x-2)=0 | | 10-9x+2x-1-3=x | | x^2+x^2=20.25 | | y=(x*x)-4x-21 | | 42b^2+b=30 | | (y*y)+3y-18=0 | | (4v+9)(7+v)=0 | | n^2-40-3n=0 |

Equations solver categories