Make an appropriate substitution and solve the equation.
-$$- \frac { 5 } { a ^ { 2 } } + \frac { 6 } { a } + 1 = 0$$
A) $\{ - 3 + \sqrt { 14 } , - 3 - \sqrt { 14 } \}$
B) $\left\{ \frac { - 3 + \sqrt { 14 } } { 5 } , \frac { - 3 - \sqrt { 14 } } { 5 } \right\}$
C) $\{ 3 + \sqrt { 14 } , 3 - \sqrt { 14 } \}$
D) $\left\{ \frac { 3 + \sqrt { 14 } } { 5 } , \frac { 3 - \sqrt { 14 } } { 5 } \right\}$

Question

Quizplus · Accepted Answer

To solve the equation, let $x = \frac{1}{a}$, which transforms the equation into a quadratic form: $-5x^2 + 6x + 1 = 0$. Solving this quadratic equation using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = -5$, $b = 6$, and $c = 1$, gives the solutions for $x$. Substituting back $x = \frac{1}{a}$ gives the solutions for $a$ as $\{ - 3 + \sqrt { 14 } , - 3 - \sqrt { 14 } \}$.

Make an Appropriate Substitution and Solve the Equation −5a2+6a+1=0- \frac { 5 } { a ^ { 2 } } + \frac { 6 } { a } + 1 = 0−a25​+a6​+1=0

Make an Appropriate Substitution and Solve the Equation $- \frac { 5 } { a ^ { 2 } } + \frac { 6 } { a } + 1 = 0$