[tex]x(x+1)= 156 \\ \\x^2+x-156=0 \\ \\a=1, \ \ b=1, \ \ c=-156\\\\\Delta =b^2-4ac = 1^2 +4\cdot1\cdot (-156) =1+624=625 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-1-\sqrt{625}}{2 }=\frac{ -1-25}{2}=\frac{-26}{2}=-13 \\ \\x_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{-1+\sqrt{625}}{2 }=\frac{ -1+25}{2}=\frac{ 24}{2}= 12\\ \\Answer: \ x=-13 \ \ or \ \ x=12[/tex]
