Question

Solve the equation. 6x=2x^2+1

Answer 1

6x = 2x^2 + 1
2x^2 - 6x + 1 = 0
$x= \frac{-(-6) \pm \sqrt{(-6)^2-(4 \times 2 \times 1)}}{2 \times 2}\\=\frac{6\pm\sqrt{36-8}}{4}\\=\frac{6\pm\sqrt{28}}{4}\\=\frac{6\pm2\sqrt{7}}{4}\\=\frac{3\pm\sqrt{7}}{2}\\=\frac{3+\sqrt{7}}{2}\,or\,\frac{3-\sqrt{7}}{2}$