3y^2+8y-78=0

Simple and best practice solution for 3y^2+8y-78=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+8y-78=0 equation:


Simplifying
3y2 + 8y + -78 = 0

Reorder the terms:
-78 + 8y + 3y2 = 0

Solving
-78 + 8y + 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'.
-26 + 2.666666667y + y2 = 0

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 2.666666667y + 26 + y2 = 0 + 26

Reorder the terms:
-26 + 26 + 2.666666667y + y2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 2.666666667y + y2 = 0 + 26
2.666666667y + y2 = 0 + 26

Combine like terms: 0 + 26 = 26
2.666666667y + y2 = 26

The y term is 2.666666667y.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667y + 1.777777780 + y2 = 26 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667y + y2 = 26 + 1.777777780

Combine like terms: 26 + 1.777777780 = 27.77777778
1.777777780 + 2.666666667y + y2 = 27.77777778

Factor a perfect square on the left side:
(y + 1.333333334)(y + 1.333333334) = 27.77777778

Calculate the square root of the right side: 5.270462767

Break this problem into two subproblems by setting 
(y + 1.333333334) equal to 5.270462767 and -5.270462767.

Subproblem 1

y + 1.333333334 = 5.270462767 Simplifying y + 1.333333334 = 5.270462767 Reorder the terms: 1.333333334 + y = 5.270462767 Solving 1.333333334 + y = 5.270462767 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + y = 5.270462767 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + y = 5.270462767 + -1.333333334 y = 5.270462767 + -1.333333334 Combine like terms: 5.270462767 + -1.333333334 = 3.937129433 y = 3.937129433 Simplifying y = 3.937129433

Subproblem 2

y + 1.333333334 = -5.270462767 Simplifying y + 1.333333334 = -5.270462767 Reorder the terms: 1.333333334 + y = -5.270462767 Solving 1.333333334 + y = -5.270462767 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + y = -5.270462767 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + y = -5.270462767 + -1.333333334 y = -5.270462767 + -1.333333334 Combine like terms: -5.270462767 + -1.333333334 = -6.603796101 y = -6.603796101 Simplifying y = -6.603796101

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.937129433, -6.603796101}

See similar equations:

| 4x^2+4x+1=5x+4 | | 20+3n= | | -8p+3=59 | | Log(x-1)=1 | | 5x-2.3=0 | | 3x^4-4x^3-12x^2+26=0 | | 12*87-25= | | x^2+16x+91=0 | | 2(4z-1)-2(2-2z)=8 | | 4.4x+1=3.4x | | x^2+3x+4x+12=0 | | B=15+Y | | 3x-1=-2x-2 | | 3-3x-36x^2= | | (4x^2-240x+3600)*x=0 | | 4x^2+1x-1=0 | | -2x+13=-27 | | 9x+3=6x+6 | | 12ab-15a-8b+10=0 | | (30-2x)(20-2x)=416 | | 13=4x^3-3x^2 | | y+9=3y-1 | | 90+2x+3x+20=180 | | 3n+2=4n-4 | | 2(x-3)-3x=-21 | | 2(-4+y)=6 | | y=5x^2-20x-19 | | 0.7n+-1.5+7.3n=14.5 | | 2x^4-2x^2-28=0 | | X+4overx=1+x | | F(x)=5cos^2(x)-10sin(x) | | x-8.6=-5.2 |

Equations solver categories