Answer:
[tex]\large\boxed{w=\dfrac{7}{6}}[/tex]
Step-by-step explanation:
[tex]w^2-\dfrac{7}{3}w+\dfrac{49}{36}=0\qquad\text{multiply both sides by 36}\\\\36w^2-36\!\!\!\!\diagup^{12}\cdot\dfrac{7}{3\!\!\!\!\diagup_1}w+36\!\!\!\!\diagup^1\cdot\dfrac{49}{36\!\!\!\!\diagup_1}=0\\\\36w^2-84w+49=0\\\\36w^2-42w-42w+49=0\\\\6w(6w-7)-7(6w-7)=0\\\\(6w-7)(6w-7)=0\\\\(6w-7)^2=0\iff 6w-7=0\qquad\text{add 7 to both sides}\\\\6w=7\qquad\text{divide both sides by 6}\\\\\boxed{w=\dfrac{7}{6}}[/tex]
