Solve y=-3x^2+8x-8f

$$y = -3 { x }^{ 2 } +8x-8f$$

Solve for f

$$f=-\frac{3x^{2}}{8}-\frac{y}{8}+x$$

Steps for Solving Linear Equation

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

$$-3x^{2}+8x-8f=y$$

Add 3x^{2} to both sides.

$$8x-8f=y+3x^{2}$$

Subtract 8x from both sides.

$$-8f=y+3x^{2}-8x$$

The equation is in standard form.

$$-8f=3x^{2}-8x+y$$

Divide both sides by -8.

$$\frac{-8f}{-8}=\frac{3x^{2}-8x+y}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$f=\frac{3x^{2}-8x+y}{-8}$$

Divide y+3x^{2}-8x by -8.

$$f=-\frac{3x^{2}}{8}-\frac{y}{8}+x$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{16-24f-3y}+4}{3}$$

$$x=\frac{\sqrt{16-24f-3y}+4}{3}$$

Solve for x

$$x=\frac{-\sqrt{16-24f-3y}+4}{3}$$

$$x=\frac{\sqrt{16-24f-3y}+4}{3}\text{, }y\leq \frac{16}{3}-8f$$