Question

What is the solution set for 12=2(3x - 7)^2 +4

Answer 1

$12=2(3x-7)^2+4 \ \ \ |-4 \\ 8=2(3x-7)^2 \ \ \ |\div 2 \\ 4=(3x-7)^2 \\ \sqrt{4}=\sqrt{(3x-7)^2} \\ 2=|3x-7| \\ 3x-7=2 \ \lor \ 3x-7=-2 \\ 3x=2+7 \ \lor \ 3x=-2+7 \\ 3x=9 \ \lor \ 3x=5 \\ x=\frac{9}{3} \ \lor \ x=\frac{5}{3} \\ x=3 \lor \ x=1 \frac{2}{3} \\ \boxed{x \in \{1 \frac{2}{3}, 3 \} }$