3y^2+2y-3=0

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


Simplifying
3y2 + 2y + -3 = 0

Reorder the terms:
-3 + 2y + 3y2 = 0

Solving
-3 + 2y + 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 + 0.6666666667y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.6666666667y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.6666666667y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.6666666667y + y2 = 0 + 1
0.6666666667y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.6666666667y + y2 = 1

The y term is 0.6666666667y.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667y + 0.1111111112 + y2 = 1 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667y + y2 = 1 + 0.1111111112

Combine like terms: 1 + 0.1111111112 = 1.1111111112
0.1111111112 + 0.6666666667y + y2 = 1.1111111112

Factor a perfect square on the left side:
(y + 0.3333333334)(y + 0.3333333334) = 1.1111111112

Calculate the square root of the right side: 1.054092553

Break this problem into two subproblems by setting 
(y + 0.3333333334) equal to 1.054092553 and -1.054092553.


Subproblem 1
y + 0.3333333334 = 1.054092553

Simplifying
y + 0.3333333334 = 1.054092553

Reorder the terms:
0.3333333334 + y = 1.054092553

Solving
0.3333333334 + y = 1.054092553

Solving for variable 'y'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + y = 1.054092553 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + y = 1.054092553 + -0.3333333334
y = 1.054092553 + -0.3333333334

Combine like terms: 1.054092553 + -0.3333333334 = 0.7207592196
y = 0.7207592196

Simplifying
y = 0.7207592196


Subproblem 2
y + 0.3333333334 = -1.054092553

Simplifying
y + 0.3333333334 = -1.054092553

Reorder the terms:
0.3333333334 + y = -1.054092553

Solving
0.3333333334 + y = -1.054092553

Solving for variable 'y'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + y = -1.054092553 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + y = -1.054092553 + -0.3333333334
y = -1.054092553 + -0.3333333334

Combine like terms: -1.054092553 + -0.3333333334 = -1.3874258864
y = -1.3874258864

Simplifying
y = -1.3874258864


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.7207592196, -1.3874258864}

See similar equations:

| -.111(x-27)+.333(x+3)=x-3 | | -6+2t=16 | | -6+2t=10 | | -(6y+4)-(-5y-8)=0 | | 8(2x-8)=2(8x+6) | | 3+8x-1=7x+50-5x | | -8(3b+1)+(25b-2)=0 | | 3.6q-1.2-4.7q=2.1q-5.3 | | 2(3+4)-9=45 | | -2(4y-3)=6 | | x-5(2x+3)=3 | | -10(a+1)=5 | | x^4+6x^3+9=0 | | 3x+5y=12 | | 2(a+5)=7 | | 2(m-3)=3 | | 2t^2+t-15=0 | | (4+3)(-3)=-9 | | 8x-6=-78 | | 3x=54-3x | | Y+12x=153 | | -2x^2+6x-9=0 | | -11+7-x=3 | | X+79=100 | | 4-x=7 | | 2(x-6)=5x+3 | | 2(x-6)=5x+3 | | 4(x+6)-2x=20 | | 8(6+-2x)+5=20 | | 4x^2+15x+16=0 | | ln(x^2)=0.7 | | lnx^2=0.7 |

Equations solver categories