#1**+2 **

Solving for a variable can be extremely daunting--especially in a multivariable equation such as \(5x^2-x=8y^2+\frac{9xy}{4}\). I have a few suggestions that may make this easier to do.

1. **Move everything to One Side of the Equation. **

This is a relatively simple step.

\(5x^2-x=8y^2+\frac{9xy}{4}\Rightarrow8y^2+\frac{9x}{4}y-5x^2+x=0\)

2. **Eliminate All Instances of Fractions or Decimals **

Fractions can be pesky, and there is no reason to make a hard situation worse. In this case, we can multiply both sides of the equation by 4 to eliminate the fractions. In a situation like this one, this is also relatively easy to do.

\(8y^2+\frac{9x}{4}y-5x^2+x=0\Rightarrow32y^2+9xy-20x^2+4x=0\)

3. **Use a Formula to Finish it Off**

This is written in the form of a quadratic, so the quadratic formula is the way to go.

\(a=32; b=9x;c=-20x^2+4x\\ y_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) | The only thing left to do is plug in the numbers. |

\(y_{1,2}=\frac{-9x\pm\sqrt{(9x)^2-4*32(-20x^2+4x)}}{2*32}\) | It is time to simplify. |

\(y_{1,2}=\frac{-9x\pm\sqrt{81x^2-128(-20x^2+4x)}}{64}\) | |

\(y_{1,2}=\frac{-9x\pm\sqrt{81x^2+2560x^2-512x}}{64}\) | |

\(y_{1,2}=\frac{-9x\pm\sqrt{2641x^2-512x}}{64}\) | I have now successfully solve for y. |

TheXSquaredFactor
Jun 27, 2018

#1**+2 **

Best Answer

Solving for a variable can be extremely daunting--especially in a multivariable equation such as \(5x^2-x=8y^2+\frac{9xy}{4}\). I have a few suggestions that may make this easier to do.

1. **Move everything to One Side of the Equation. **

This is a relatively simple step.

\(5x^2-x=8y^2+\frac{9xy}{4}\Rightarrow8y^2+\frac{9x}{4}y-5x^2+x=0\)

2. **Eliminate All Instances of Fractions or Decimals **

Fractions can be pesky, and there is no reason to make a hard situation worse. In this case, we can multiply both sides of the equation by 4 to eliminate the fractions. In a situation like this one, this is also relatively easy to do.

\(8y^2+\frac{9x}{4}y-5x^2+x=0\Rightarrow32y^2+9xy-20x^2+4x=0\)

3. **Use a Formula to Finish it Off**

This is written in the form of a quadratic, so the quadratic formula is the way to go.

\(a=32; b=9x;c=-20x^2+4x\\ y_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) | The only thing left to do is plug in the numbers. |

\(y_{1,2}=\frac{-9x\pm\sqrt{(9x)^2-4*32(-20x^2+4x)}}{2*32}\) | It is time to simplify. |

\(y_{1,2}=\frac{-9x\pm\sqrt{81x^2-128(-20x^2+4x)}}{64}\) | |

\(y_{1,2}=\frac{-9x\pm\sqrt{81x^2+2560x^2-512x}}{64}\) | |

\(y_{1,2}=\frac{-9x\pm\sqrt{2641x^2-512x}}{64}\) | I have now successfully solve for y. |

TheXSquaredFactor
Jun 27, 2018