4y^2-12y+3=0

Simple and best practice solution for 4y^2-12y+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 4y^2-12y+3=0 equation:


Simplifying
4y2 + -12y + 3 = 0

Reorder the terms:
3 + -12y + 4y2 = 0

Solving
3 + -12y + 4y2 = 0

Solving for variable 'y'.

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

Divide each side by '4'.
0.75 + -3y + y2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -3y + -0.75 + y2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -3y + y2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -3y + y2 = 0 + -0.75
-3y + y2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-3y + y2 = -0.75

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 = -0.75 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -0.75 + 2.25

Combine like terms: -0.75 + 2.25 = 1.5
2.25 + -3y + y2 = 1.5

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

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1.224744871 and -1.224744871.

Subproblem 1

y + -1.5 = 1.224744871 Simplifying y + -1.5 = 1.224744871 Reorder the terms: -1.5 + y = 1.224744871 Solving -1.5 + y = 1.224744871 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 = 1.224744871 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 1.224744871 + 1.5 y = 1.224744871 + 1.5 Combine like terms: 1.224744871 + 1.5 = 2.724744871 y = 2.724744871 Simplifying y = 2.724744871

Subproblem 2

y + -1.5 = -1.224744871 Simplifying y + -1.5 = -1.224744871 Reorder the terms: -1.5 + y = -1.224744871 Solving -1.5 + y = -1.224744871 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 = -1.224744871 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -1.224744871 + 1.5 y = -1.224744871 + 1.5 Combine like terms: -1.224744871 + 1.5 = 0.275255129 y = 0.275255129 Simplifying y = 0.275255129

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.724744871, 0.275255129}

See similar equations:

| -2x^2+6y^2+12= | | (x-9)(x+9)=4(-x-15) | | x^2+y^2+8x-2y-8=0 | | 60-3x=15x+22 | | x^2+(-3)x+(-10)x=0 | | 8-9x=19-16x | | 14x^2+33x=5 | | 6-10x=23-17x | | 12-7x=66-28x | | 89-3x=2x-24 | | (0.66)X+20=100 | | x-5-14=0 | | (-0.75)X+2=(0.50)X+6 | | 5a^2+12a+7=0 | | 128-5x=4x+11 | | 3y+16y=-5 | | 3y^2-13y+4=0 | | 5a^2-3a-14=0 | | (.25)X+26=36 | | 5b^2+2b-3=0 | | y+23+6+33333=2223454 | | y+5=9 | | 7n^2+10n+3=0 | | 4y^2-20y+23=0 | | 4s^2+13s+3=0 | | k^2+14k+48=0 | | 11x+8=9x+13 | | 6x+11=6x+2x | | -28-6=12-10x | | 8x-8=80 | | 7x-4=29 | | 10+5x=135 |

Equations solver categories