4y^2+y-6=0

Simple and best practice solution for 4y^2+y-6=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+y-6=0 equation:


Simplifying
4y2 + y + -6 = 0

Reorder the terms:
-6 + y + 4y2 = 0

Solving
-6 + y + 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'.
-1.5 + 0.25y + y2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.25y + 1.5 + y2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.25y + y2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.25y + y2 = 0 + 1.5
0.25y + y2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.25y + y2 = 1.5

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25y + 0.25 + y2 = 1.5 + 0.25

Reorder the terms:
0.25 + 0.25y + y2 = 1.5 + 0.25

Combine like terms: 1.5 + 0.25 = 1.75
0.25 + 0.25y + y2 = 1.75

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(y + 0.5) equal to 1.322875656 and -1.322875656.

Subproblem 1

y + 0.5 = 1.322875656 Simplifying y + 0.5 = 1.322875656 Reorder the terms: 0.5 + y = 1.322875656 Solving 0.5 + y = 1.322875656 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 1.322875656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 1.322875656 + -0.5 y = 1.322875656 + -0.5 Combine like terms: 1.322875656 + -0.5 = 0.822875656 y = 0.822875656 Simplifying y = 0.822875656

Subproblem 2

y + 0.5 = -1.322875656 Simplifying y + 0.5 = -1.322875656 Reorder the terms: 0.5 + y = -1.322875656 Solving 0.5 + y = -1.322875656 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -1.322875656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -1.322875656 + -0.5 y = -1.322875656 + -0.5 Combine like terms: -1.322875656 + -0.5 = -1.822875656 y = -1.822875656 Simplifying y = -1.822875656

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.822875656, -1.822875656}

See similar equations:

| 70+1x=8x | | 8v+4v-v-7v=12 | | 3X+3+72=180 | | 6(x-9)=6+7x | | (9p^4+7p^3-2)+(6p-5p+6)= | | 1/k^2=0.25 | | -6v-20=-6v+21 | | 17x+504= | | (3n-4)+n=28 | | 116=4(-1+6m) | | 14r+4r-18r+2r+3r=10 | | 3.00x=-9 | | 2(6x-5)+22= | | 75x+300=100x+200 | | 2-4y=4y-4 | | x^3-5x^2-8x=0 | | -6(x-3)-20=-2 | | -7h-7h-h=-15 | | 3(x+6)=12-5 | | X^3=x^2+7x | | 12t(t-5)=0 | | 2(8n+3)+10= | | 2q-q=6 | | 21x-28=8x-48+10 | | 17a-12a=20 | | (7(9-z)/6)=-z | | 58m+129=658 | | -0.6x+0.7x-1=1 | | 24-3x=-7(3-6x) | | t^6+6t^3=27 | | -7.7-4y-7.7-2y=-5y-7.5 | | (x-4)*(x+3)=(x-2)*(x-1) |

Equations solver categories