3y^2+16y-3=0

Simple and best practice solution for 3y^2+16y-3=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+16y-3=0 equation: 


Simplifying
3y2 + 16y + -3 = 0

Reorder the terms:
-3 + 16y + 3y2 = 0

Solving
-3 + 16y + 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'.
-1 + 5.333333333y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 5.333333333y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + 5.333333333y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5.333333333y + y2 = 0 + 1
5.333333333y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
5.333333333y + y2 = 1

The y term is 5.333333333y.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333y + 7.111111113 + y2 = 1 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333y + y2 = 1 + 7.111111113

Combine like terms: 1 + 7.111111113 = 8.111111113
7.111111113 + 5.333333333y + y2 = 8.111111113

Factor a perfect square on the left side:
(y + 2.666666667)(y + 2.666666667) = 8.111111113

Calculate the square root of the right side: 2.848001249

Break this problem into two subproblems by setting 
(y + 2.666666667) equal to 2.848001249 and -2.848001249.


Subproblem 1
y + 2.666666667 = 2.848001249

Simplifying
y + 2.666666667 = 2.848001249

Reorder the terms:
2.666666667 + y = 2.848001249

Solving
2.666666667 + y = 2.848001249

Solving for variable 'y'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + y = 2.848001249 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + y = 2.848001249 + -2.666666667
y = 2.848001249 + -2.666666667

Combine like terms: 2.848001249 + -2.666666667 = 0.181334582
y = 0.181334582

Simplifying
y = 0.181334582


Subproblem 2
y + 2.666666667 = -2.848001249

Simplifying
y + 2.666666667 = -2.848001249

Reorder the terms:
2.666666667 + y = -2.848001249

Solving
2.666666667 + y = -2.848001249

Solving for variable 'y'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + y = -2.848001249 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + y = -2.848001249 + -2.666666667
y = -2.848001249 + -2.666666667

Combine like terms: -2.848001249 + -2.666666667 = -5.514667916
y = -5.514667916

Simplifying
y = -5.514667916


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.181334582, -5.514667916}

See similar equations:

| 3.2x-0.75=0.2x-2.25 | | 7-8x=42-x | | 2m+4=4m+5 | | 1428=204*x | | (5x+12)(7x-4)=50 | | 4-5x=x-13 | | 3(6j+1)= | | 6x-16=62+4x | | 3cos^2x-2cosx=0 | | -16h^3+80h^2y-100hy^2=0 | | (4+t)+2= | | 8y+7=7y-6 | | 2z+15=9 | | 4-5a=x-13 | | 8a+7=39 | | 20y^2+10y=0 | | 9x+5=6x+47 | | 6d-9=36 | | 7-6x=a-16 | | 36v^2-49d^2=0 | | 3cosx=cosx-2 | | 5(2x-1)-(10x-6)=-7 | | (7t+1)(7)= | | F(x)=9x^2+5x+2 | | 3.4x-6.8+7x=7.4x-21.2 | | x=-.92y | | 1-5-9i= | | -24x-12=42-3x | | 7g+6g-4= | | .868x=-.8y | | 19v-3v+4v=20 | | 20-2=6 |

Equations solver categories