Answer
$\displaystyle \frac{4+\sqrt{6}}{5}\approx 1.290$
$\displaystyle \frac{4-\sqrt{6}}{5}\approx 0.310$
Work Step by Step
$5x^{2}-8x+2=0$
Use the quadratic formula:
(For $ax^{2}+bx+c=0,\ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ )
$x=\displaystyle \frac{-(-8)\pm\sqrt{(-8)^{2}-4(5)(2)}}{2(5)}$
$=\displaystyle \frac{8\pm\sqrt{24}}{10}=\frac{8\pm\sqrt{4\times 6}}{10}$
$=\displaystyle \frac{8\pm 2\sqrt{6}}{10}=\frac{2(4\pm\sqrt{6})}{2(5)}$
$x=\displaystyle \frac{4\pm\sqrt{6}}{5}$
Solutions:
$\displaystyle \frac{4+\sqrt{6}}{5}\approx 1.290$ and
$\displaystyle \frac{4-\sqrt{6}}{5}\approx 0.310$.
