(2x+3)(x-12)=0

Solution for (2x+3)(x-12)=0 equation:

(2x+3)(x-12)=0

We multiply parentheses ..

(+2x^2-24x+3x-36)=0

We get rid of parentheses

2x^2-24x+3x-36=0

We add all the numbers together, and all the variables

2x^2-21x-36=0

a = 2; b = -21; c = -36;
Δ = b2-4ac
Δ = -212-4·2·(-36)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-27}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+27}{2*2}=\frac{48}{4}
=12
$