3n^2+8-23n=0

Simple and best practice solution for 3n^2+8-23n=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+8-23n=0 equation: 


Simplifying
3n2 + 8 + -23n = 0

Reorder the terms:
8 + -23n + 3n2 = 0

Solving
8 + -23n + 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'.
2.666666667 + -7.666666667n + n2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -7.666666667n + -2.666666667 + n2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -7.666666667n + n2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -7.666666667n + n2 = 0 + -2.666666667
-7.666666667n + n2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-7.666666667n + n2 = -2.666666667

The n term is -7.666666667n.  Take half its coefficient (-3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
-7.666666667n + 14.69444445 + n2 = -2.666666667 + 14.69444445

Reorder the terms:
14.69444445 + -7.666666667n + n2 = -2.666666667 + 14.69444445

Combine like terms: -2.666666667 + 14.69444445 = 12.027777783
14.69444445 + -7.666666667n + n2 = 12.027777783

Factor a perfect square on the left side:
(n + -3.833333334)(n + -3.833333334) = 12.027777783

Calculate the square root of the right side: 3.468108675

Break this problem into two subproblems by setting 
(n + -3.833333334) equal to 3.468108675 and -3.468108675.


Subproblem 1
n + -3.833333334 = 3.468108675

Simplifying
n + -3.833333334 = 3.468108675

Reorder the terms:
-3.833333334 + n = 3.468108675

Solving
-3.833333334 + n = 3.468108675

Solving for variable 'n'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + n = 3.468108675 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + n = 3.468108675 + 3.833333334
n = 3.468108675 + 3.833333334

Combine like terms: 3.468108675 + 3.833333334 = 7.301442009
n = 7.301442009

Simplifying
n = 7.301442009


Subproblem 2
n + -3.833333334 = -3.468108675

Simplifying
n + -3.833333334 = -3.468108675

Reorder the terms:
-3.833333334 + n = -3.468108675

Solving
-3.833333334 + n = -3.468108675

Solving for variable 'n'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + n = -3.468108675 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + n = -3.468108675 + 3.833333334
n = -3.468108675 + 3.833333334

Combine like terms: -3.468108675 + 3.833333334 = 0.365224659
n = 0.365224659

Simplifying
n = 0.365224659


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.301442009, 0.365224659}

See similar equations:

| 5x+3=20x | | 3x-10.4=x+8.8 | | 9y^3-x^2y= | | 1/4(2x-4)=7 | | 2(11-4*-2)=38 | | 8.46/1.5= | | log[3x-7](25)=2 | | 5(x+9)=-6x+1 | | 2x+4x^2-30x= | | 8+5y=17 | | x+6+12=24 | | X^3+2x=150 | | 4x+1=12x | | 35+2+x=9(3) | | -14x-28y=14 | | 10x+20y=-3 | | 9d+10=2d-11 | | 3*(4d+1)-9d=6*2-d | | 12x+16y=28 | | 3x+1=12x | | x+x+x+3=18 | | -213+4y=623 | | 3x+10y+19+17x-11y-14= | | -6x-8y=-14 | | 6(2x-1)=4x-10 | | d^3+4d-7=0 | | 7r=5r+14 | | 2(9n-1)+(n+6)=60 | | -3(9--3)+9= | | X^2+y^2+18x+12y+36=0 | | x+3(4+x)=20 | | 7x-3+x=13 |

Equations solver categories