# Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. 3x(x−1)=x+63x(x−1)=x+6

Question
Equations and inequalities
Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. $$3x(x−1)=x+63x(x−1)=x+6$$

2021-01-28
$$3x(x-l)=2+6$$
Apply the distributive property $$3x^{2}-3x=x+6$$
Subtract «+ 6 from each side $$3x^{2}-3x—x-6=0$$
$$3x^{2}-4x-6=0$$
By the quadratic formula $$x=\frac{-(-4)\pm \sqrt{(-4)^2-4(3)(-6)}}{2(3)}$$
$$x=\frac{4\pm\sqrt88}6=\frac{4\pm\sqrt4*22}6)$$
$$x=\frac{4}{6}\pm\frac{2\sqrt{22}}6$$
$$x=\frac{2}{3}\pm \frac{\sqrt{22}}{3}$$

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