2y^2-3y=7

Simple and best practice solution for 2y^2-3y=7 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 2y^2-3y=7 equation:


Simplifying
2y2 + -3y = 7

Reorder the terms:
-3y + 2y2 = 7

Solving
-3y + 2y2 = 7

Solving for variable 'y'.

Reorder the terms:
-7 + -3y + 2y2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -3y + 2y2 = 0

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

Divide each side by '2'.
-3.5 + -1.5y + y2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -1.5y + 3.5 + y2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -1.5y + y2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -1.5y + y2 = 0 + 3.5
-1.5y + y2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-1.5y + y2 = 3.5

The y term is -1.5y.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5y + 0.5625 + y2 = 3.5 + 0.5625

Reorder the terms:
0.5625 + -1.5y + y2 = 3.5 + 0.5625

Combine like terms: 3.5 + 0.5625 = 4.0625
0.5625 + -1.5y + y2 = 4.0625

Factor a perfect square on the left side:
(y + -0.75)(y + -0.75) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(y + -0.75) equal to 2.015564437 and -2.015564437.

Subproblem 1

y + -0.75 = 2.015564437 Simplifying y + -0.75 = 2.015564437 Reorder the terms: -0.75 + y = 2.015564437 Solving -0.75 + y = 2.015564437 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = 2.015564437 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 2.015564437 + 0.75 y = 2.015564437 + 0.75 Combine like terms: 2.015564437 + 0.75 = 2.765564437 y = 2.765564437 Simplifying y = 2.765564437

Subproblem 2

y + -0.75 = -2.015564437 Simplifying y + -0.75 = -2.015564437 Reorder the terms: -0.75 + y = -2.015564437 Solving -0.75 + y = -2.015564437 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = -2.015564437 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -2.015564437 + 0.75 y = -2.015564437 + 0.75 Combine like terms: -2.015564437 + 0.75 = -1.265564437 y = -1.265564437 Simplifying y = -1.265564437

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.765564437, -1.265564437}

See similar equations:

| 9x+2y=-26 | | 4*2*.6= | | 5z+3=2z-12 | | (m+3)(8m-1)(4m-3)=12m-1m | | 4a^2b^2-16ab^3+8ab^2c=0 | | 4(2x-3)-5(4x-1)=6 | | 3t^2-19t-14=0 | | xln(x)-9+3ln(x)-3x=0 | | 7x-1=8x+6 | | -3x^2-11x-6=0 | | (2x-5)(x+3)=0 | | -5(x+7)-45=8-58 | | 5x^2+30x+50=0 | | 2y^2+5y-3=0 | | 16x-19=2(6x-6)+4x-7 | | 9a+10=100 | | 1/3=1/2+f | | r-5.1=-8.6 | | 3a+5=20 | | 7x-5y=15 | | 1.6q-1.5-0.7=.1q-5.7 | | 2x+8=3y | | 3x+8=2y | | simplfy-4(6n-4)+3n= | | 5x^2+4x=4 | | f=80t-16t^2 | | -4(6n-4)+3n= | | 15-3Y=3+9Y | | 5+3x=x+27 | | 15-6x=11+4x | | -3(x+2)=5-x | | 3(6z-1)-5(z+5)=8(z+1) |

Equations solver categories