Answer to Question #225493 in Algebra for Arun kumar

Question

Find all x ∈ R that solve this equation: 123 = x

Answer 1

$$123 = x (2x (3x − 3) − 2) + 100 + 20 + 3$$

$$x (2x (3x − 3) − 2)=0$$

$$2x(3x^2-3x-1)=0$$

$$x=0\ or\ 3x^2-3x-1=0$$

$$x=\dfrac{3\pm\sqrt{(-3)^2-4(3)(-1)}}{2(3)}=\dfrac{3\pm\sqrt{21}}{6}$$

$$x\in \{0, \dfrac{3-\sqrt{21}}{6}, \dfrac{3+\sqrt{21}}{6}\}$$