X(4x+9)=96

Solution for X(4x+9)=96 equation:

X(4X+9)=96

We move all terms to the left:

X(4X+9)-(96)=0

We multiply parentheses

4X^2+9X-96=0

a = 4; b = 9; c = -96;
Δ = b2-4ac
Δ = 92-4·4·(-96)
Δ = 1617
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1617}=\sqrt{49*33}=\sqrt{49}*\sqrt{33}=7\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7\sqrt{33}}{2*4}=\frac{-9-7\sqrt{33}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7\sqrt{33}}{2*4}=\frac{-9+7\sqrt{33}}{8}
$