3y^2-23y-30=0

Simple and best practice solution for 3y^2-23y-30=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^2-23y-30=0 equation: 


Simplifying
3y2 + -23y + -30 = 0

Reorder the terms:
-30 + -23y + 3y2 = 0

Solving
-30 + -23y + 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'.
-10 + -7.666666667y + y2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -7.666666667y + 10 + y2 = 0 + 10

Reorder the terms:
-10 + 10 + -7.666666667y + y2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -7.666666667y + y2 = 0 + 10
-7.666666667y + y2 = 0 + 10

Combine like terms: 0 + 10 = 10
-7.666666667y + y2 = 10

The y term is -7.666666667y.  Take half its coefficient (-3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
-7.666666667y + 14.69444445 + y2 = 10 + 14.69444445

Reorder the terms:
14.69444445 + -7.666666667y + y2 = 10 + 14.69444445

Combine like terms: 10 + 14.69444445 = 24.69444445
14.69444445 + -7.666666667y + y2 = 24.69444445

Factor a perfect square on the left side:
(y + -3.833333334)(y + -3.833333334) = 24.69444445

Calculate the square root of the right side: 4.969350506

Break this problem into two subproblems by setting 
(y + -3.833333334) equal to 4.969350506 and -4.969350506.


Subproblem 1
y + -3.833333334 = 4.969350506

Simplifying
y + -3.833333334 = 4.969350506

Reorder the terms:
-3.833333334 + y = 4.969350506

Solving
-3.833333334 + y = 4.969350506

Solving for variable 'y'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + y = 4.969350506 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + y = 4.969350506 + 3.833333334
y = 4.969350506 + 3.833333334

Combine like terms: 4.969350506 + 3.833333334 = 8.80268384
y = 8.80268384

Simplifying
y = 8.80268384


Subproblem 2
y + -3.833333334 = -4.969350506

Simplifying
y + -3.833333334 = -4.969350506

Reorder the terms:
-3.833333334 + y = -4.969350506

Solving
-3.833333334 + y = -4.969350506

Solving for variable 'y'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + y = -4.969350506 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + y = -4.969350506 + 3.833333334
y = -4.969350506 + 3.833333334

Combine like terms: -4.969350506 + 3.833333334 = -1.136017172
y = -1.136017172

Simplifying
y = -1.136017172


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.80268384, -1.136017172}

See similar equations:

| 8*y-9=7/2*y | | 4.5xz=27 | | (5xy^4)(-3x^2y^3)= | | 1/7y=-8 | | 6=8n-2n | | -42+6x=38+11x | | W=p(v-l)forl | | 21=5(d-7)-4 | | 1x/x^3-7x | | 4a+1.20=7.20 | | 4x-9y=37 | | 7.5y-3.5= | | x(7x+2)=2x^2-6x+4 | | Q/7=5 | | a-23/-28=-7 | | -3x+4y=29 | | -3+y+y=-3 | | 3(x-3)+13=2(x+8) | | 6(x+1)+2(x+1)= | | (x-9)(x+7)(x-3)=0 | | 9*5/9(F-32)*9= | | 5(x-2)=22 | | X+2=-26+11 | | 20x+ky-10=0 | | 5e^3x=8e^6x | | 7/4=3y | | (5x+6)+(3x-12)= | | 40y-20y= | | 2x+9y=3 | | 9(2k+3)+2=11(k-4.1) | | 8(z+2)-2(z-2)=2(z-4)+3(z-4) | | f(c+3)=4x-3 |

Equations solver categories