(3x+6)(2x-7)=0

Solution for (3x+6)(2x-7)=0 equation:

(3x+6)(2x-7)=0

We multiply parentheses ..

(+6x^2-21x+12x-42)=0

We get rid of parentheses

6x^2-21x+12x-42=0

We add all the numbers together, and all the variables

6x^2-9x-42=0

a = 6; b = -9; c = -42;
Δ = b2-4ac
Δ = -92-4·6·(-42)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-33}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+33}{2*6}=\frac{42}{12}
=3+1/2
$