3y^2-14y-240=0

Simple and best practice solution for 3y^2-14y-240=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 3y^2-14y-240=0 equation: 


Simplifying
3y2 + -14y + -240 = 0

Reorder the terms:
-240 + -14y + 3y2 = 0

Solving
-240 + -14y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
-80 + -4.666666667y + y2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -4.666666667y + 80 + y2 = 0 + 80

Reorder the terms:
-80 + 80 + -4.666666667y + y2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -4.666666667y + y2 = 0 + 80
-4.666666667y + y2 = 0 + 80

Combine like terms: 0 + 80 = 80
-4.666666667y + y2 = 80

The y term is -4.666666667y.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667y + 5.444444448 + y2 = 80 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667y + y2 = 80 + 5.444444448

Combine like terms: 80 + 5.444444448 = 85.444444448
5.444444448 + -4.666666667y + y2 = 85.444444448

Factor a perfect square on the left side:
(y + -2.333333334)(y + -2.333333334) = 85.444444448

Calculate the square root of the right side: 9.243616416

Break this problem into two subproblems by setting 
(y + -2.333333334) equal to 9.243616416 and -9.243616416.


Subproblem 1
y + -2.333333334 = 9.243616416

Simplifying
y + -2.333333334 = 9.243616416

Reorder the terms:
-2.333333334 + y = 9.243616416

Solving
-2.333333334 + y = 9.243616416

Solving for variable 'y'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + y = 9.243616416 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + y = 9.243616416 + 2.333333334
y = 9.243616416 + 2.333333334

Combine like terms: 9.243616416 + 2.333333334 = 11.57694975
y = 11.57694975

Simplifying
y = 11.57694975


Subproblem 2
y + -2.333333334 = -9.243616416

Simplifying
y + -2.333333334 = -9.243616416

Reorder the terms:
-2.333333334 + y = -9.243616416

Solving
-2.333333334 + y = -9.243616416

Solving for variable 'y'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + y = -9.243616416 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + y = -9.243616416 + 2.333333334
y = -9.243616416 + 2.333333334

Combine like terms: -9.243616416 + 2.333333334 = -6.910283082
y = -6.910283082

Simplifying
y = -6.910283082


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.57694975, -6.910283082}

See similar equations:

| 81k^2-25m^2= | | 28x^2+87x+54=0 | | -2m+5=4m+10 | | x-5=0.1 | | 8g/4=g+9 | | x^2+7x-72=0 | | (5+3i)(2+6i)= | | -15=2y-7 | | 6-x=19 | | -12+4c=6c-(6+5) | | .07x+899.1-x=60 | | -r=8 | | 14-6u=-11-u | | -(x)+3=0 | | 12k^2-28k-5=0 | | (4a^3+16a^2)-(9a-36)=0 | | 6-3(x+2)=4(x-7) | | 5c+3=46.5 | | -4.2+3x=3 | | -(-b-4)=12 | | 16v^3+52v^2-48v=0 | | X+(-20)=36 | | 6t=4t-18 | | x^2+4xy-12y^2= | | 0.25=0.5c | | -4(-4z)=80 | | 4x^2-21x=-20 | | 6p-24+6=4p-46 | | 6p-24+6=4p-47 | | 2a^2+7a=15 | | 25-5p=19-4p | | -9x+3=5-11x |

Equations solver categories