4(x+3)(2x-9)=0

Solution for 4(x+3)(2x-9)=0 equation:

4(x+3)(2x-9)=0

We multiply parentheses ..

4(+2x^2-9x+6x-27)=0

We multiply parentheses

8x^2-36x+24x-108=0

We add all the numbers together, and all the variables

8x^2-12x-108=0

a = 8; b = -12; c = -108;
Δ = b2-4ac
Δ = -122-4·8·(-108)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-60}{2*8}=\frac{-48}{16}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+60}{2*8}=\frac{72}{16}
=4+1/2
$