#### Answer

$y=\dfrac{3}{2}\pm\dfrac{7\sqrt{5}}{10}$

#### Work Step by Step

$5y^{2}-15y=1$
Take out common factor $5$ from the left side of the equation:
$5(y^{2}-3y)=1$
Take the $5$ to divide the right side of the equation:
$y^{2}-3y=\dfrac{1}{5}$
Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. In this case, $b=-3$
$y^{2}-3y+\Big(\dfrac{-3}{2}\Big)^{2}=\dfrac{1}{5}+\Big(\dfrac{-3}{2}\Big)^{2}$
$y^{2}-3y+\dfrac{9}{4}=\dfrac{1}{5}+\dfrac{9}{4}$
$y^{2}-3y+\dfrac{9}{4}=\dfrac{49}{20}$
Factor the expression on the left side of the equation, which is a perfect square trinomial:
$\Big(y-\dfrac{3}{2}\Big)^{2}=\dfrac{49}{20}$
Take the square root of both sides of the equation:
$\sqrt{\Big(y-\dfrac{3}{2}\Big)^{2}}=\sqrt{\dfrac{49}{20}}$
$y-\dfrac{3}{2}=\pm\dfrac{7}{\sqrt{20}}$
Solve for $y$:
$y=\dfrac{3}{2}\pm\dfrac{7}{\sqrt{20}}=\dfrac{3}{2}\pm\dfrac{7\sqrt{20}}{20}=\dfrac{3}{2}\pm\dfrac{7\sqrt{5}}{10}$