2(9x^2-11x-24)=0

Solution for 2(9x^2-11x-24)=0 equation:

2(9x^2-11x-24)=0

We multiply parentheses

18x^2-22x-48=0

a = 18; b = -22; c = -48;
Δ = b2-4ac
Δ = -222-4·18·(-48)
Δ = 3940
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:

$\sqrt{\Delta}=\sqrt{3940}=\sqrt{4*985}=\sqrt{4}*\sqrt{985}=2\sqrt{985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{985}}{2*18}=\frac{22-2\sqrt{985}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{985}}{2*18}=\frac{22+2\sqrt{985}}{36}
$