Solve 4x^2+3x-j=0

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

Solve for j

$$j=x\left(4x+3\right)$$

Steps for Solving Linear Equation

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

$$3x-j=-4x^{2}$$

Subtract 3x from both sides.

$$-j=-4x^{2}-3x$$

Divide both sides by -1.

$$\frac{-j}{-1}=-\frac{x\left(4x+3\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$j=-\frac{x\left(4x+3\right)}{-1}$$

Divide -x\left(3+4x\right) by -1.

$$j=x\left(4x+3\right)$$

Solve for x (complex solution)

$$x=\frac{\sqrt{16j+9}-3}{8}$$

$$x=\frac{-\sqrt{16j+9}-3}{8}$$

Solve for x

$$x=\frac{\sqrt{16j+9}-3}{8}$$

$$x=\frac{-\sqrt{16j+9}-3}{8}\text{, }j\geq -\frac{9}{16}$$