9(-4x+1)(6x-36)=0

Solution for 9(-4x+1)(6x-36)=0 equation:

9(-4x+1)(6x-36)=0

We multiply parentheses ..

9(-24x^2+144x+6x-36)=0

We multiply parentheses

-216x^2+1296x+54x-324=0

We add all the numbers together, and all the variables

-216x^2+1350x-324=0

a = -216; b = 1350; c = -324;
Δ = b2-4ac
Δ = 13502-4·(-216)·(-324)
Δ = 1542564
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1542564}=1242$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1350)-1242}{2*-216}=\frac{-2592}{-432}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1350)+1242}{2*-216}=\frac{-108}{-432}
=1/4
$