Solve 1-f(x)=9x^2-4x+3

$$1 - f ( x ) = 9 x ^ { 2 } - 4 x + 3$$

Solve for f

$$f=-9x+4-\frac{2}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 1 from both sides.

$$-fx=9x^{2}-4x+3-1$$

Subtract 1 from 3 to get 2.

$$-fx=9x^{2}-4x+2$$

The equation is in standard form.

$$\left(-x\right)f=9x^{2}-4x+2$$

Divide both sides by -x.

$$\frac{\left(-x\right)f}{-x}=\frac{9x^{2}-4x+2}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$f=\frac{9x^{2}-4x+2}{-x}$$

Divide 9x^{2}-4x+2 by -x.

$$f=-9x+4-\frac{2}{x}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{f^{2}-8f-56}}{18}-\frac{f}{18}+\frac{2}{9}$$

$$x=\frac{\sqrt{f^{2}-8f-56}}{18}-\frac{f}{18}+\frac{2}{9}$$

Solve for x

$$x=-\frac{\sqrt{f^{2}-8f-56}}{18}-\frac{f}{18}+\frac{2}{9}$$

$$x=\frac{\sqrt{f^{2}-8f-56}}{18}-\frac{f}{18}+\frac{2}{9}\text{, }f\geq 6\sqrt{2}+4\text{ or }f\leq 4-6\sqrt{2}$$