(x2+x+1)(x2+x+2)-12=10
[tex]\left(x\cdot \:2+x+1\right)\left(x\cdot \:2+x+2\right)-12 =\left(3x+1\right)\left(3x+2\right)-12 =9x^2+9x+2-12 =9x^2+9x-10[/tex]
[tex]9x^2+9x-10=10[/tex]
[tex]9x^2+9x-10-10=10-10[/tex]
[tex]9x^2+9x-20=0[/tex]
[tex]\frac{-9+\sqrt{9^2-4\cdot \:9\left(-20\right)}}{2\cdot \:9}[/tex]
[tex]=\frac{-9+\sqrt{9^2+4\cdot \:9\cdot \:20}}{2\cdot \:9}[/tex]
[tex]\sqrt{9^2+4\cdot \:9\cdot \:20} =\sqrt{81+4\cdot \:9\cdot \:20} =\sqrt{81+720}=\sqrt{801}[/tex]
[tex]=\frac{-9+\sqrt{801}}{18}[/tex]
[tex]\sqrt{801}=3\sqrt{89}[/tex]
[tex]=\frac{-9+3\sqrt{89}}{18}[/tex]
[tex]=\frac{-3+\sqrt{89}}{6}[/tex]
[tex]\frac{-9-\sqrt{9^2-4\cdot \:9\left(-20\right)}}{2\cdot \:9}[/tex]
[tex]\sqrt{9^2+4\cdot \:9\cdot \:20} =\sqrt{81+4\cdot \:9\cdot \:20} =\sqrt{81+720} =\sqrt{801}[/tex]
[tex]=\frac{-9-\sqrt{801}}{2\cdot \:9}[/tex]
[tex]=\frac{-9-3\sqrt{89}}{18}[/tex]
[tex]=-\frac{3\left(3+\sqrt{89}\right)}{18}[/tex]
[tex]=-\frac{3+\sqrt{89}}{6}[/tex]
[tex]x=\frac{-3+\sqrt{89}}{6},\:x=-\frac{3+\sqrt{89}}{6}[/tex]
