Solve f:x+4x-1=x+15

$$f : x + 4 x - 1 = x + 15$$

Solve for f

$$f=-x\left(3x-16\right)$$

$$x\neq 0$$

Solution Steps

Multiply both sides of the equation by x.

$$f+4xx+x\left(-1\right)=xx+x\times 15$$

Multiply x and x to get x^{2}.

$$f+4x^{2}+x\left(-1\right)=xx+x\times 15$$

Multiply x and x to get x^{2}.

$$f+4x^{2}+x\left(-1\right)=x^{2}+x\times 15$$

Subtract 4x^{2} from both sides.

$$f+x\left(-1\right)=x^{2}+x\times 15-4x^{2}$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$f+x\left(-1\right)=-3x^{2}+x\times 15$$

Subtract x\left(-1\right) from both sides.

$$f=-3x^{2}+x\times 15-x\left(-1\right)$$

Combine x\times 15 and -x\left(-1\right) to get 16x.

$$f=-3x^{2}+16x$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{\sqrt{64-3f}+8}{3}\text{, }&\text{unconditionally}\\x=\frac{-\sqrt{64-3f}+8}{3}\text{, }&f\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{-\sqrt{64-3f}+8}{3}\text{, }&f\neq 0\text{ and }f\leq \frac{64}{3}\\x=\frac{\sqrt{64-3f}+8}{3}\text{, }&f\leq \frac{64}{3}\end{matrix}\right.$$