Question

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

Answer 1

`x_(1) = -1 - \sqrt{(2)/(3)}  ; x_(2) = -1 +\sqrt{(2)/(3)}`

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 = (-b\pm√(b^2-4ac))/(2a)`

a = 3; b = 6; y = 1

`x = (-6\pm√(6^2 - 4* 3 *1))/(2* 3)`

`x = (-6\pm√(36-12))/(6)`

`x = (-6\pm√(24))/(6)`

`x = (-6\pm √(4*6))/(6)`

`x = (-6\pm 2√(2))/(6)`

`x = -1 \pm \sqrt{(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.