Answer:
4x^2 + 9x + 4 = 0
Using the quadratic formula:
x = [-9 +- sqrt(81 - (-64)] / 2 * 4
x = [-9 +- sqrt (145)] / 8
So, the solution is your second answer:
negative 9 plus or minus the square root of 145 divided by 8.
ANSWER

EXPLANATION
Since the altitude, |GJ| bisects the base of the triangle, it follows that, the triangle is an isosceles triangle.
This implies that,.

In terms of x, we have the equation.

We now group like terms to obtain,

This implies that,

Let us divide through by 2 to get,

We can see from the diagram that,

We substitute x=5 to get,

This simplifies to,

Calcualte the ratio 32/48=2/3