4(x+6)(2x-3)=0

Solution for 4(x+6)(2x-3)=0 equation:

4(x+6)(2x-3)=0

We multiply parentheses ..

4(+2x^2-3x+12x-18)=0

We multiply parentheses

8x^2-12x+48x-72=0

We add all the numbers together, and all the variables

8x^2+36x-72=0

a = 8; b = 36; c = -72;
Δ = b2-4ac
Δ = 362-4·8·(-72)
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{-(36)-60}{2*8}=\frac{-96}{16}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+60}{2*8}=\frac{24}{16}
=1+1/2
$