9y-4y^2=3

Simple and best practice solution for 9y-4y^2=3 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 9y-4y^2=3 equation:


Simplifying
9y + -4y2 = 3

Solving
9y + -4y2 = 3

Solving for variable 'y'.

Reorder the terms:
-3 + 9y + -4y2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 9y + -4y2 = 0

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

Divide each side by '-4'.
0.75 + -2.25y + y2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2.25y + -0.75 + y2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -2.25y + y2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2.25y + y2 = 0 + -0.75
-2.25y + y2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-2.25y + y2 = -0.75

The y term is -2.25y.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25y + 1.265625 + y2 = -0.75 + 1.265625

Reorder the terms:
1.265625 + -2.25y + y2 = -0.75 + 1.265625

Combine like terms: -0.75 + 1.265625 = 0.515625
1.265625 + -2.25y + y2 = 0.515625

Factor a perfect square on the left side:
(y + -1.125)(y + -1.125) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(y + -1.125) equal to 0.718070331 and -0.718070331.

Subproblem 1

y + -1.125 = 0.718070331 Simplifying y + -1.125 = 0.718070331 Reorder the terms: -1.125 + y = 0.718070331 Solving -1.125 + y = 0.718070331 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + y = 0.718070331 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + y = 0.718070331 + 1.125 y = 0.718070331 + 1.125 Combine like terms: 0.718070331 + 1.125 = 1.843070331 y = 1.843070331 Simplifying y = 1.843070331

Subproblem 2

y + -1.125 = -0.718070331 Simplifying y + -1.125 = -0.718070331 Reorder the terms: -1.125 + y = -0.718070331 Solving -1.125 + y = -0.718070331 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + y = -0.718070331 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + y = -0.718070331 + 1.125 y = -0.718070331 + 1.125 Combine like terms: -0.718070331 + 1.125 = 0.406929669 y = 0.406929669 Simplifying y = 0.406929669

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.843070331, 0.406929669}

See similar equations:

| 5y-13=2+5(10) | | -0.2x=0.38 | | -3(y-5)=-4y | | 2z+32=-2z | | 2(x+3)-3(4x-5)=7x+1 | | Sin(Pi/c) | | 192x^3+3y^3=0 | | 10x^2+26x-3= | | 100x+90y=2680 | | 6x-3=6x+3 | | 3c-15=7-c | | 7a=62 | | 5+5/6x=x/3-1 | | x+15+x+25+40=180 | | Z^3+5z+3z^2+1-4-2z^2= | | 5(290-0.6(0))+3(0)=1450 | | 13=-4x+4 | | X^4+64=20 | | 12x+56=140 | | -6(-x-2)=12 | | 0.5(x+5)-0.8(x+1)=8 | | 1-1/x=30/x^2 | | 7x+49=154 | | (4s-3)(5s+5)= | | 9.6p+4=2.6p+39 | | 20x^2-x=1 | | 4(x-3)+y=-11 | | -8.9-10.11=77.44 | | 3x+2x+x=96 | | 3xy=2x+4y+z | | 1450-0.6y+3y=1450 | | 0.129x=0.043(3x+3) |

Equations solver categories