Solve 14x+19=3xx-33a

$$14 x + 19 = 3 x x - 33 a$$

Solve for a

$$a=\frac{x^{2}}{11}-\frac{14x}{33}-\frac{19}{33}$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$14x+19=3x^{2}-33a$$

Swap sides so that all variable terms are on the left hand side.

$$3x^{2}-33a=14x+19$$

Subtract 3x^{2} from both sides.

$$-33a=14x+19-3x^{2}$$

The equation is in standard form.

$$-33a=19+14x-3x^{2}$$

Divide both sides by -33.

$$\frac{-33a}{-33}=\frac{19+14x-3x^{2}}{-33}$$

Dividing by -33 undoes the multiplication by -33.

$$a=\frac{19+14x-3x^{2}}{-33}$$

Divide 14x+19-3x^{2} by -33.

$$a=\frac{x^{2}}{11}-\frac{14x}{33}-\frac{19}{33}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{99a+106}+7}{3}$$

$$x=\frac{\sqrt{99a+106}+7}{3}$$

Solve for x

$$x=\frac{-\sqrt{99a+106}+7}{3}$$

$$x=\frac{\sqrt{99a+106}+7}{3}\text{, }a\geq -\frac{106}{99}$$