Solve 2x^2+6x-k=0

$$2 x ^ { 2 } + 6 x - k = 0$$

Solve for k

$$k=2x\left(x+3\right)$$

Steps for Solving Linear Equation

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

$$6x-k=-2x^{2}$$

Subtract 6x from both sides.

$$-k=-2x^{2}-6x$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide -2x\left(3+x\right) by -1.

$$k=2x\left(x+3\right)$$

Solve for x (complex solution)

$$x=\frac{\sqrt{2k+9}-3}{2}$$

$$x=\frac{-\sqrt{2k+9}-3}{2}$$

Solve for x

$$x=\frac{\sqrt{2k+9}-3}{2}$$

$$x=\frac{-\sqrt{2k+9}-3}{2}\text{, }k\geq -\frac{9}{2}$$