Answer:
[tex]x_{1} = -1 - \sqrt{\frac{2}{3}} ; x_{2} = -1 +\sqrt{\frac{2}{3}}[/tex]
Step-by-step explanation:
-6x -1 + 5x² = 8x² Move all terms to the right-hand side
0 = 8x² - 5x² + 6x +1 Combine like terms
3x² + 6x + 1 = 0
Apply the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = 3; b = 6; y = 1
[tex]x = \frac{-6\pm\sqrt{6^2 - 4\times 3 \times1}}{2\times 3}[/tex]
[tex]x = \frac{-6\pm\sqrt{36-12}}{6}[/tex]
[tex]x = \frac{-6\pm\sqrt{24}}{6}[/tex]
[tex]x = \frac{-6\pm \sqrt{4\times6}}{6}[/tex]
[tex]x = \frac{-6\pm 2\sqrt{2}}{6}[/tex]
[tex]x = -1 \pm \sqrt{\frac{2}{3}}[/tex]
[tex]x_{1} = -1 +\sqrt{\frac{{2}}{3}}; x_{2} = 1 -\sqrt{\frac{{2}}{3}}[/tex]
The graph below shows the roots at x₁ =-1.816 and x₂ = -0.184.
