Solve 3x^2+(p-11)x+6=0

$$3 x ^ { 2 } + ( p - 11 ) x + 6 = 0$$

Solve for p

$$p=-3x+11-\frac{6}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply p-11 by x.

$$3x^{2}+px-11x+6=0$$

Subtract 3x^{2} from both sides. Anything subtracted from zero gives its negation.

$$px-11x+6=-3x^{2}$$

Add 11x to both sides.

$$px+6=-3x^{2}+11x$$

Subtract 6 from both sides.

$$px=-3x^{2}+11x-6$$

The equation is in standard form.

$$xp=-3x^{2}+11x-6$$

Divide both sides by x.

$$\frac{xp}{x}=\frac{\left(3-x\right)\left(3x-2\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$p=\frac{\left(3-x\right)\left(3x-2\right)}{x}$$

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

$$p=-3x+11-\frac{6}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{p^{2}-22p+49}-p+11}{6}$$

$$x=\frac{-\sqrt{p^{2}-22p+49}-p+11}{6}$$

Solve for x

$$x=\frac{\sqrt{p^{2}-22p+49}-p+11}{6}$$

$$x=\frac{-\sqrt{p^{2}-22p+49}-p+11}{6}\text{, }p\geq 6\sqrt{2}+11\text{ or }p\leq 11-6\sqrt{2}$$