216(4x-9)(-x+4)=0

Solution for 216(4x-9)(-x+4)=0 equation:

216(4x-9)(-x+4)=0

We add all the numbers together, and all the variables

216(4x-9)(-1x+4)=0

We multiply parentheses ..

216(-4x^2+16x+9x-36)=0

We multiply parentheses

-864x^2+3456x+1944x-7776=0

We add all the numbers together, and all the variables

-864x^2+5400x-7776=0

a = -864; b = 5400; c = -7776;
Δ = b2-4ac
Δ = 54002-4·(-864)·(-7776)
Δ = 2286144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2286144}=1512$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5400)-1512}{2*-864}=\frac{-6912}{-1728}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5400)+1512}{2*-864}=\frac{-3888}{-1728}
=2+1/4
$