Question

Solve: -6x-1+5x^2=8x^2

Answer 1

Answer:

$x_{1} = -1 - \sqrt{\frac{2}{3}} ; x_{2} = -1 +\sqrt{\frac{2}{3}}$

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

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a = 3; b = 6; y = 1

$x = \frac{-6\pm\sqrt{6^2 - 4\times 3 \times1}}{2\times 3}$

$x = \frac{-6\pm\sqrt{36-12}}{6}$

$x = \frac{-6\pm\sqrt{24}}{6}$

$x = \frac{-6\pm \sqrt{4\times6}}{6}$

$x = \frac{-6\pm 2\sqrt{2}}{6}$

$x = -1 \pm \sqrt{\frac{2}{3}}$

$x_{1} = -1 +\sqrt{\frac{{2}}{3}}; x_{2} = 1 -\sqrt{\frac{{2}}{3}}$

The graph below shows the roots at x₁ =-1.816 and x₂ = -0.184.