Solve y^2-8ky+24k+16=0

$$y ^ { 2 } - 8 k y + 24 k + 16 = 0$$

Solve for k

$$k=-\frac{y^{2}+16}{8\left(3-y\right)}$$

$$y\neq 3$$

Steps for Solving Linear Equation

Subtract y^{2} from both sides. Anything subtracted from zero gives its negation.

$$-8ky+24k+16=-y^{2}$$

Subtract 16 from both sides.

$$-8ky+24k=-y^{2}-16$$

Combine all terms containing k.

$$\left(-8y+24\right)k=-y^{2}-16$$

The equation is in standard form.

$$\left(24-8y\right)k=-y^{2}-16$$

Divide both sides by -8y+24.

$$\frac{\left(24-8y\right)k}{24-8y}=\frac{-y^{2}-16}{24-8y}$$

Dividing by -8y+24 undoes the multiplication by -8y+24.

$$k=\frac{-y^{2}-16}{24-8y}$$

Divide -y^{2}-16 by -8y+24.

$$k=-\frac{y^{2}+16}{8\left(3-y\right)}$$

Solve for y (complex solution)

$$y=2\sqrt{4k^{2}-6k-4}+4k$$

$$y=-2\sqrt{4k^{2}-6k-4}+4k$$

Solve for y

$$y=2\sqrt{4k^{2}-6k-4}+4k$$

$$y=-2\sqrt{4k^{2}-6k-4}+4k\text{, }k\leq -\frac{1}{2}\text{ or }k\geq 2$$