Answer
$y = \frac{8 \pm \sqrt{14}}{10}$
Work Step by Step
$Find$ $all$ $real$ $solutions$ $of$ $the$ $quadratic$ $equation:$
$10y^2-16y+5=0$
Use the Quadratic Equation Formula: $x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}$
$10y^2-16y+5$
$a = 10, b = -16, c = 5$
$y = \frac{-(-16) \pm \sqrt {(-16)^2- 4(10 \times 5)}}{2(10)}$
$y = \frac{16 \pm \sqrt {256- 200}}{20}$
$y = \frac{16 \pm \sqrt {56}}{20}$
$y = \frac{16 \pm \sqrt {56}}{20}$
[Note: $\sqrt{56} = \sqrt{4\times14} = \sqrt{4}\times\sqrt{14}$ = $2\sqrt{14}$]
$y=\frac{16 \pm 2\sqrt {14}}{20}$
$y=\frac{2(8\pm\sqrt{14})}{20}$
$y = \frac{8 \pm \sqrt{14}}{10}$
