3y^2+9y+4=0

Simple and best practice solution for 3y^2+9y+4=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+9y+4=0 equation:


Simplifying
3y2 + 9y + 4 = 0

Reorder the terms:
4 + 9y + 3y2 = 0

Solving
4 + 9y + 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'.
1.333333333 + 3y + y2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 3y + -1.333333333 + y2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 3y + y2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 3y + y2 = 0 + -1.333333333
3y + y2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
3y + y2 = -1.333333333

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = -1.333333333 + 2.25

Reorder the terms:
2.25 + 3y + y2 = -1.333333333 + 2.25

Combine like terms: -1.333333333 + 2.25 = 0.916666667
2.25 + 3y + y2 = 0.916666667

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 0.916666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(y + 1.5) equal to 0.957427108 and -0.957427108.

Subproblem 1

y + 1.5 = 0.957427108 Simplifying y + 1.5 = 0.957427108 Reorder the terms: 1.5 + y = 0.957427108 Solving 1.5 + y = 0.957427108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 0.957427108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 0.957427108 + -1.5 y = 0.957427108 + -1.5 Combine like terms: 0.957427108 + -1.5 = -0.542572892 y = -0.542572892 Simplifying y = -0.542572892

Subproblem 2

y + 1.5 = -0.957427108 Simplifying y + 1.5 = -0.957427108 Reorder the terms: 1.5 + y = -0.957427108 Solving 1.5 + y = -0.957427108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -0.957427108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -0.957427108 + -1.5 y = -0.957427108 + -1.5 Combine like terms: -0.957427108 + -1.5 = -2.457427108 y = -2.457427108 Simplifying y = -2.457427108

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-0.542572892, -2.457427108}

See similar equations:

| 7(3-6)=6(4+t) | | y^2=12 | | 4a^2=48-4a | | -18-k=6+18k | | 4n^2=8n | | (20x)-40=180 | | 7y+12x-2=o | | 7a^2-36a+5=0 | | -3(-2+x)=60 | | 15r^2+52r+32=0 | | 2m+3=8 | | -9-x=-6 | | 4z-15=-8z-27 | | 1/4(5-2)=h/2 | | 9y^2+4-12y=0 | | 0.7x^2-0.3x-1=0 | | 3k-6=18 | | 8-5a=3a+5a | | 2.4=-0.8x+3.2 | | (-9+3n^6+3n^5)+(2n^6+5n^5+6)= | | 2x^3+14x^2+2x+14= | | 6+10n=-174 | | 4v^2+4v=80 | | x^6-7x^5-6x^4= | | 4y-7=27 | | 19c=152 | | 14=-p+8 | | 2a+5=25 | | 0.7p+4.6=5d+8 | | -5(-3)+-7+-2(-3)+-2=12 | | 144=-9y | | -9x-2=4 |

Equations solver categories