# Use the discriminant to predict the nature of the roots, then use the quadratic formula to find the roots. 9x^2 + 3x - 8 = 0

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The discriminant of the equation `9x^2 + 3x - 8=0`

would be defined by `b^2 - 4ac`

Therefore: b = 3, a = 9, and c = -8

So, the discriminant is `3^2 - 4(9)(-8)`

`9 + 288 = 297`

Since discriminant is `>=0` then we will have **real roots**.

`(-3+-sqrt(297))/(2(9))`

`(-3+-sqrt(297))/18` Simplify `sqrt(297)`

`sqrt(297) =sqrt(9)*sqrt(33)` = `3sqrt(33)`

So thiswil give us: `(-3+-3sqrt(33))/18`

Since everything has factor of 3, we can cancel to give us:

`(-1+-sqrt(33))/6`

so the **roots are**: `x = (-1+-sqrt(33))/6`

` `

`9x^2 + 3x - 8 = 0`

`a=9` `b=3 ` `c=-8 ` `b^2-4ac`

`3^2-4(9)(-8)`

`9+288=297 ` **297 is the discriminant since it is bigger than 0 it has 2 real solutions**. To find the roots use:

`(-b+-sqrt(b^2-4ac))/(2a)`

`(-3+-sqrt(297))/(2(9))`

`(-3+-sqrt(297))/(18)`

`(-3-sqrt(297))/(18) ` `x=-1.12`

`(-3+sqrt(297))/(18) ` `x=0.79`