(3x+12)(2x-9)=0

Solution for (3x+12)(2x-9)=0 equation:

(3x+12)(2x-9)=0

We multiply parentheses ..

(+6x^2-27x+24x-108)=0

We get rid of parentheses

6x^2-27x+24x-108=0

We add all the numbers together, and all the variables

6x^2-3x-108=0

a = 6; b = -3; c = -108;
Δ = b2-4ac
Δ = -32-4·6·(-108)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-51}{2*6}=\frac{-48}{12}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+51}{2*6}=\frac{54}{12}
=4+1/2
$