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

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

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

We multiply parentheses ..

(+21x^2+18x-49x-42)=0

We get rid of parentheses

21x^2+18x-49x-42=0

We add all the numbers together, and all the variables

21x^2-31x-42=0

a = 21; b = -31; c = -42;
Δ = b2-4ac
Δ = -312-4·21·(-42)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-67}{2*21}=\frac{-36}{42}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+67}{2*21}=\frac{98}{42}
=2+1/3
$