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

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

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

We multiply parentheses ..

(+12x^2-6x+24x-12)=0

We get rid of parentheses

12x^2-6x+24x-12=0

We add all the numbers together, and all the variables

12x^2+18x-12=0

a = 12; b = 18; c = -12;
Δ = b2-4ac
Δ = 182-4·12·(-12)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*12}=\frac{-48}{24}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*12}=\frac{12}{24}
=1/2
$