$$ \begin{aligned} 3(2x-5)+34(3x+1) &= \frac{5}{6}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot3(2x-5)+6\cdot34(3x+1) &= 6\cdot\frac{5}{6}&& \text{cancel out the denominators} \\[1 em]36x-90+612x+204 &= 5&& \text{simplify left side} \\[1 em]648x+114 &= 5&& \text{ move 114 to the right } \\[1 em]648x &= 5-114&& \\[1 em]648x &= -109&& \text{ divide both sides by $ 648 $ } \\[1 em]x &= -\frac{109}{648}&& \\[1 em] \end{aligned} $$

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