Answer:
The roots are:
[tex] \frac{-1+ \sqrt{8} }{3} and \frac{-1- \sqrt{8} }{3} [/tex]
Explanation:
First we would need to put the equation in standard form which is as follows:
ax² + bx + c = 0
This can be done as follows:
9x² + 6x + 1 = 8
Subtract 8 from both sides and combine like terms to reach the following:
9x² + 6x - 7 = 0
By comparison:
a = 9
b = 6
c = -7
Now, to get the roots, we would need to use the quadratic formula attached in the images.
By substitution, we would find that:
either x = [tex] \frac{-6+ \sqrt{(6)^2-4(9)(-7)} }{2(9)} = \frac{-1 + \sqrt{8} }{3} [/tex]
or x = [tex] \frac{-6- \sqrt{(6)^2-4(9)(-7)} }{2(9)} = \frac{-1 - \sqrt{8} }{3} [/tex]
Hope this helps :)
