3y^2-12y-1=0

Simple and best practice solution for 3y^2-12y-1=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^2-12y-1=0 equation:


Simplifying
3y2 + -12y + -1 = 0

Reorder the terms:
-1 + -12y + 3y2 = 0

Solving
-1 + -12y + 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'.
-0.3333333333 + -4y + y2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -4y + 0.3333333333 + y2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -4y + y2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -4y + y2 = 0 + 0.3333333333
-4y + y2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-4y + y2 = 0.3333333333

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 0.3333333333 + 4

Reorder the terms:
4 + -4y + y2 = 0.3333333333 + 4

Combine like terms: 0.3333333333 + 4 = 4.3333333333
4 + -4y + y2 = 4.3333333333

Factor a perfect square on the left side:
(y + -2)(y + -2) = 4.3333333333

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
(y + -2) equal to 2.081665999 and -2.081665999.

Subproblem 1

y + -2 = 2.081665999 Simplifying y + -2 = 2.081665999 Reorder the terms: -2 + y = 2.081665999 Solving -2 + y = 2.081665999 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 2.081665999 + 2 Combine like terms: -2 + 2 = 0 0 + y = 2.081665999 + 2 y = 2.081665999 + 2 Combine like terms: 2.081665999 + 2 = 4.081665999 y = 4.081665999 Simplifying y = 4.081665999

Subproblem 2

y + -2 = -2.081665999 Simplifying y + -2 = -2.081665999 Reorder the terms: -2 + y = -2.081665999 Solving -2 + y = -2.081665999 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -2.081665999 + 2 Combine like terms: -2 + 2 = 0 0 + y = -2.081665999 + 2 y = -2.081665999 + 2 Combine like terms: -2.081665999 + 2 = -0.081665999 y = -0.081665999 Simplifying y = -0.081665999

Solution

The solution to the problem is based on the solutions from the subproblems. y = {4.081665999, -0.081665999}

See similar equations:

| z-9z=4z-4-z | | 1+e^4x+1=20 | | 5-b=2b-19 | | 16-4x=x | | 25-x=5x+6 | | 15u^2-23u+4=0 | | x^2-2x+0.48=0 | | -2(y+6)=-6y-16 | | y-3=5x-1 | | 12=2x+3+7x | | 9y+35=2(y-7) | | -2v+10=2(v-7) | | 6-r+2s=8 | | 13-59+X=63-27-5X | | 6x^5-12x^2-16x+2=0 | | 13X-59+X=63-27-5X | | 9(v+5)=3v+21 | | 5(x-4)-11=14x-67 | | 13X+X+5X=63-27+59 | | 5c+9=25c-9 | | -8(v+2)+4v+5=8v+12 | | 4w-5=36 | | 7x-6(8+7x)= | | 2x-6=13+x-4 | | Xsquared+11=36 | | (2x+4)*log*8=(2-3x)*log*7 | | 6+.5x=9 | | l=4w-5 | | 18a^2b+39a^2b+-17ab^2+-11a^2b+53ab^2= | | Y+2Y+3Y-Y=14+29-13 | | 3x^2-13x+2=-2 | | 6+.5x=12 |

Equations solver categories