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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+6x^2+12x-9x-18)=0

We get rid of parentheses

6x^2+12x-9x-18=0

We add all the numbers together, and all the variables

6x^2+3x-18=0

a = 6; b = 3; c = -18;
Δ = b2-4ac
Δ = 32-4·6·(-18)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-21}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+21}{2*6}=\frac{18}{12}
=1+1/2
$