The roots of the equation $2x^2 - 5x - 4 = -x^2 - 7x + 6$ can be written in the form $x = \frac{m \pm \sqrt{n}}{p}$, where $m$, $n$, and $p$ are positive integers with a greatest common divisor of $1$. What is the value of $n$?
\(x = \frac{m \pm \sqrt{n}}{p}\)
2x^2 - 5x - 4 = -x^2 -7x + 6 rearrange as
3x^2 + 2x - 10 = 0
The discriminant =
(2)^2 - 4(3)(-10) =
4 + 120 =
124
sqrt (124) =sqrt (31 * 4) = 2 sqrt (31)
So
x = [ -2 ± 2 sqrt (31) ] / ( 2 * 3) = [ -1 ± sqrt (31)] / 3
n = 31
+817 
