Solve kx^2-10x+6k=5,w

$$k x ^ { 2 } - 10 x + 6 k = 5 , w$$

Solve for k (complex solution)

$$k=\frac{5\left(2x+1\right)}{x^{2}+6}$$

$$x\neq -\sqrt{6}i\text{ and }x\neq \sqrt{6}i$$

Steps for Solving Linear Equation

Add 10x to both sides.

$$kx^{2}+6k=5+10x$$

Combine all terms containing k.

$$\left(x^{2}+6\right)k=5+10x$$

The equation is in standard form.

$$\left(x^{2}+6\right)k=10x+5$$

Divide both sides by x^{2}+6.

$$\frac{\left(x^{2}+6\right)k}{x^{2}+6}=\frac{10x+5}{x^{2}+6}$$

Dividing by x^{2}+6 undoes the multiplication by x^{2}+6.

$$k=\frac{10x+5}{x^{2}+6}$$

Divide 5+10x by x^{2}+6.

$$k=\frac{5\left(2x+1\right)}{x^{2}+6}$$

Solve for k

$$k=\frac{5\left(2x+1\right)}{x^{2}+6}$$

Steps for Solving Linear Equation

Add 10x to both sides.

$$kx^{2}+6k=5+10x$$

Combine all terms containing k.

$$\left(x^{2}+6\right)k=5+10x$$

The equation is in standard form.

$$\left(x^{2}+6\right)k=10x+5$$

Divide both sides by x^{2}+6.

$$\frac{\left(x^{2}+6\right)k}{x^{2}+6}=\frac{10x+5}{x^{2}+6}$$

Dividing by x^{2}+6 undoes the multiplication by x^{2}+6.

$$k=\frac{10x+5}{x^{2}+6}$$

Divide 5+10x by x^{2}+6.

$$k=\frac{5\left(2x+1\right)}{x^{2}+6}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{25+5k-6k^{2}}+5}{k}\text{; }x=\frac{-\sqrt{25+5k-6k^{2}}+5}{k}\text{, }&k\neq 0\\x=-\frac{1}{2}\text{, }&k=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{\left(5-2k\right)\left(3k+5\right)}+5}{k}\text{; }x=\frac{-\sqrt{\left(5-2k\right)\left(3k+5\right)}+5}{k}\text{, }&k\neq 0\text{ and }k\geq -\frac{5}{3}\text{ and }k\leq \frac{5}{2}\\x=-\frac{1}{2}\text{, }&k=0\end{matrix}\right.$$