[tex]\displaystyle x^2+x=90 \\ x^2+x-90=0 \\ a=1,=1,c=-90 \\ \Delta=b^2-4ac=1^2-4 \cdot 1 \cdot (-90)=1+360=361 \\ x_1= \frac{-1+ \sqrt{361} }{2 \cdot 1} = \frac{-1+19}{2} = \frac{18}{2} =9 \\ \\ x_2= \frac{-1- \sqrt{361} }{2 \cdot1} = \frac{-1-19}{2} = \frac{-20}{2} =-10[/tex]