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