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

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

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

We multiply parentheses ..

(+21x^2+18x-42x-36)=0

We get rid of parentheses

21x^2+18x-42x-36=0

We add all the numbers together, and all the variables

21x^2-24x-36=0

a = 21; b = -24; c = -36;
Δ = b2-4ac
Δ = -242-4·21·(-36)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-60}{2*21}=\frac{-36}{42}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+60}{2*21}=\frac{84}{42}
=2
$