Solve (k-3)x^2-(k+4)x+30=0

$$( k - 3 ) x ^ { 2 } - ( k + 4 ) x + 30 = 0$$

Solve for k

$$k=-\frac{30-4x-3x^{2}}{x\left(x-1\right)}$$

$$x\neq 1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply k-3 by x^{2}.

$$kx^{2}-3x^{2}-\left(k+4\right)x+30=0$$

Use the distributive property to multiply k+4 by x.

$$kx^{2}-3x^{2}-\left(kx+4x\right)+30=0$$

To find the opposite of kx+4x, find the opposite of each term.

$$kx^{2}-3x^{2}-kx-4x+30=0$$

Add 3x^{2} to both sides. Anything plus zero gives itself.

$$kx^{2}-kx-4x+30=3x^{2}$$

Add 4x to both sides.

$$kx^{2}-kx+30=3x^{2}+4x$$

Subtract 30 from both sides.

$$kx^{2}-kx=3x^{2}+4x-30$$

Combine all terms containing k.

$$\left(x^{2}-x\right)k=3x^{2}+4x-30$$

Divide both sides by x^{2}-x.

$$\frac{\left(x^{2}-x\right)k}{x^{2}-x}=\frac{3x^{2}+4x-30}{x^{2}-x}$$

Dividing by x^{2}-x undoes the multiplication by x^{2}-x.

$$k=\frac{3x^{2}+4x-30}{x^{2}-x}$$

Divide 3x^{2}+4x-30 by x^{2}-x.

$$k=\frac{3x^{2}+4x-30}{x\left(x-1\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{k^{2}-112k+376}+k+4}{2\left(k-3\right)}\text{; }x=\frac{-\sqrt{k^{2}-112k+376}+k+4}{2\left(k-3\right)}\text{, }&k\neq 3\\x=\frac{30}{7}\text{, }&k=3\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{k^{2}-112k+376}+k+4}{2\left(k-3\right)}\text{; }x=\frac{-\sqrt{k^{2}-112k+376}+k+4}{2\left(k-3\right)}\text{, }&\left(k\neq 3\text{ and }k\leq 56-2\sqrt{690}\right)\text{ or }k\geq 2\sqrt{690}+56\\x=\frac{30}{7}\text{, }&k=3\end{matrix}\right.$$