Solve 4t^2/2t+3=x/y

$$\frac { 4 t ^ { 2 } } { 2 t + 3 } = \frac { x } { y }$$

Solve for x

$$x=\frac{4yt^{2}}{2t+3}$$

$$t\neq -\frac{3}{2}\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y\left(2t+3\right), the least common multiple of 2t+3,y.

$$y\times 4t^{2}=\left(2t+3\right)x$$

Use the distributive property to multiply 2t+3 by x.

$$y\times 4t^{2}=2tx+3x$$

Swap sides so that all variable terms are on the left hand side.

$$2tx+3x=y\times 4t^{2}$$

Combine all terms containing x.

$$\left(2t+3\right)x=y\times 4t^{2}$$

The equation is in standard form.

$$\left(2t+3\right)x=4yt^{2}$$

Divide both sides by 2t+3.

$$\frac{\left(2t+3\right)x}{2t+3}=\frac{4yt^{2}}{2t+3}$$

Dividing by 2t+3 undoes the multiplication by 2t+3.

$$x=\frac{4yt^{2}}{2t+3}$$

Solve for t (complex solution)

$$t=\frac{\sqrt{x\left(x+12y\right)}+x}{4y}$$

$$t=\frac{-\sqrt{x\left(x+12y\right)}+x}{4y}\text{, }y\neq 0$$

Solve for t

$$t=\frac{\sqrt{x\left(x+12y\right)}+x}{4y}$$

$$t=\frac{-\sqrt{x\left(x+12y\right)}+x}{4y}\text{, }y\neq 0\text{ and }\left(x\geq 0\text{ or }x\leq -12y\right)\text{ and }\left(x\leq 0\text{ or }x\geq -12y\right)$$