6y^2-19y=10

Simple and best practice solution for 6y^2-19y=10 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 6y^2-19y=10 equation:


Simplifying
6y2 + -19y = 10

Reorder the terms:
-19y + 6y2 = 10

Solving
-19y + 6y2 = 10

Solving for variable 'y'.

Reorder the terms:
-10 + -19y + 6y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -19y + 6y2 = 0

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

Divide each side by '6'.
-1.666666667 + -3.166666667y + y2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -3.166666667y + 1.666666667 + y2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -3.166666667y + y2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -3.166666667y + y2 = 0 + 1.666666667
-3.166666667y + y2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-3.166666667y + y2 = 1.666666667

The y term is -3.166666667y.  Take half its coefficient (-1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
-3.166666667y + 2.506944447 + y2 = 1.666666667 + 2.506944447

Reorder the terms:
2.506944447 + -3.166666667y + y2 = 1.666666667 + 2.506944447

Combine like terms: 1.666666667 + 2.506944447 = 4.173611114
2.506944447 + -3.166666667y + y2 = 4.173611114

Factor a perfect square on the left side:
(y + -1.583333334)(y + -1.583333334) = 4.173611114

Calculate the square root of the right side: 2.042941779

Break this problem into two subproblems by setting 
(y + -1.583333334) equal to 2.042941779 and -2.042941779.

Subproblem 1

y + -1.583333334 = 2.042941779 Simplifying y + -1.583333334 = 2.042941779 Reorder the terms: -1.583333334 + y = 2.042941779 Solving -1.583333334 + y = 2.042941779 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + y = 2.042941779 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + y = 2.042941779 + 1.583333334 y = 2.042941779 + 1.583333334 Combine like terms: 2.042941779 + 1.583333334 = 3.626275113 y = 3.626275113 Simplifying y = 3.626275113

Subproblem 2

y + -1.583333334 = -2.042941779 Simplifying y + -1.583333334 = -2.042941779 Reorder the terms: -1.583333334 + y = -2.042941779 Solving -1.583333334 + y = -2.042941779 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + y = -2.042941779 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + y = -2.042941779 + 1.583333334 y = -2.042941779 + 1.583333334 Combine like terms: -2.042941779 + 1.583333334 = -0.459608445 y = -0.459608445 Simplifying y = -0.459608445

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.626275113, -0.459608445}

See similar equations:

| 4x+1=3x+4 | | 14x-7+3x-3=13x-4+3x | | 28x^2-3x-15=0 | | 2y+8=5x | | 2x-15-3y=0 | | 3x+6(2x^2)=0 | | -11/15x=3 | | 3x-(7x-5)=-47 | | 2x-4=f | | -5.1-6z-6.7-z=-6z+2.9 | | 2x+2x+x+3+x+3= | | N+4=3 | | X=-35+4y | | 8=(c/-4)=12 | | 5(x-4)-1=-7x+4 | | 4-(7-k)=2(k+3) | | ((K-3)/4)=10 | | 2x+4x=5x-5 | | (x^2)-(y^2)=4 | | a/-3=6 | | 5/a=3/10 | | -5(x-5)=6-4x | | 6[3-(4+6x)]-2x=-8+2(1+-19x) | | 9x=15-3y | | 10/11=8/y | | 16x-10=-14x-2(x+5) | | 1/N=10/50 | | 6x-8=x-3 | | 4x+28-28=-36-28 | | 3/10=12/z | | 5t-26=28t | | 3+a=-4 |

Equations solver categories