4n^2-3n-20=0

Simple and best practice solution for 4n^2-3n-20=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 4n^2-3n-20=0 equation:


Simplifying
4n2 + -3n + -20 = 0

Reorder the terms:
-20 + -3n + 4n2 = 0

Solving
-20 + -3n + 4n2 = 0

Solving for variable 'n'.

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

Divide each side by '4'.
-5 + -0.75n + n2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -0.75n + 5 + n2 = 0 + 5

Reorder the terms:
-5 + 5 + -0.75n + n2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -0.75n + n2 = 0 + 5
-0.75n + n2 = 0 + 5

Combine like terms: 0 + 5 = 5
-0.75n + n2 = 5

The n term is -0.75n.  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.
-0.75n + 0.140625 + n2 = 5 + 0.140625

Reorder the terms:
0.140625 + -0.75n + n2 = 5 + 0.140625

Combine like terms: 5 + 0.140625 = 5.140625
0.140625 + -0.75n + n2 = 5.140625

Factor a perfect square on the left side:
(n + -0.375)(n + -0.375) = 5.140625

Calculate the square root of the right side: 2.267294643

Break this problem into two subproblems by setting 
(n + -0.375) equal to 2.267294643 and -2.267294643.

Subproblem 1

n + -0.375 = 2.267294643 Simplifying n + -0.375 = 2.267294643 Reorder the terms: -0.375 + n = 2.267294643 Solving -0.375 + n = 2.267294643 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + n = 2.267294643 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + n = 2.267294643 + 0.375 n = 2.267294643 + 0.375 Combine like terms: 2.267294643 + 0.375 = 2.642294643 n = 2.642294643 Simplifying n = 2.642294643

Subproblem 2

n + -0.375 = -2.267294643 Simplifying n + -0.375 = -2.267294643 Reorder the terms: -0.375 + n = -2.267294643 Solving -0.375 + n = -2.267294643 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + n = -2.267294643 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + n = -2.267294643 + 0.375 n = -2.267294643 + 0.375 Combine like terms: -2.267294643 + 0.375 = -1.892294643 n = -1.892294643 Simplifying n = -1.892294643

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.642294643, -1.892294643}

See similar equations:

| 9-6=3(2x-5) | | 4x=135+3y | | 1296=x^2 | | 0.2p-1.2=-0.2p | | -5(d-5)+20=15 | | 4(2x-5)=64 | | 4x+x(2)+12-4+2x= | | x^2+5n+6=0 | | 3x=4(-3x+6) | | 3m=228 | | x+8=1+2x | | -32=r^5 | | -20=8+7b | | 20t+7=-6(4t-5)+2t+(5t+1)+x | | -8x+12+2x=-30 | | 4r=756 | | 6x+11=8x+34 | | 3x(2)+5x-17+6x+20= | | 2x(4)=8 | | 3n+2(n+8)=6 | | 2x+12=2x+2x | | 24-2(4p+8)=56 | | 9=1+1.4ln(x+1) | | ln(x+4)+ln(x-5)=2ln(x) | | ln(2x+1)=2 | | 2x+1(x)=105 | | 9p+4-p-20=56 | | 3r=42 | | 5x-9=3+-6x | | -3y+10=-5 | | 30x^2-19x-63=0 | | 1.1+ln*x^2=6 |

Equations solver categories