\(x\cdot\left(x+1\right):2=153\)
\(\Rightarrow x\left(x+1\right)=153\cdot2\)
\(\Rightarrow x^2+x=306\)
\(\Rightarrow x^2+x-306=0\)
\(\Rightarrow x^2+18x-17x-306=0\)
\(\Rightarrow x\left(x+18\right)-17\left(x+18\right)=0\)
\(\Rightarrow\left(x-17\right)\left(x+18\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=17\\x=-18\end{matrix}\right.\)
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