Solve 4x^2+5x-k=0

$$4 x ^ { 2 } + 5 x - k = 0$$

Solve for k

$$k=x\left(4x+5\right)$$

Steps for Solving Linear Equation

Subtract 4x^{2} from both sides. Anything subtracted from zero gives its negation.

$$5x-k=-4x^{2}$$

Subtract 5x from both sides.

$$-k=-4x^{2}-5x$$

Divide both sides by -1.

$$\frac{-k}{-1}=-\frac{x\left(4x+5\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$k=-\frac{x\left(4x+5\right)}{-1}$$

Divide -x\left(5+4x\right) by -1.

$$k=x\left(4x+5\right)$$

Solve for x (complex solution)

$$x=\frac{\sqrt{16k+25}-5}{8}$$

$$x=\frac{-\sqrt{16k+25}-5}{8}$$

Solve for x

$$x=\frac{\sqrt{16k+25}-5}{8}$$

$$x=\frac{-\sqrt{16k+25}-5}{8}\text{, }k\geq -\frac{25}{16}$$