(3x-9)(7x+7)=0

Solution for (3x-9)(7x+7)=0 equation:

(3x-9)(7x+7)=0

We multiply parentheses ..

(+21x^2+21x-63x-63)=0

We get rid of parentheses

21x^2+21x-63x-63=0

We add all the numbers together, and all the variables

21x^2-42x-63=0

a = 21; b = -42; c = -63;
Δ = b2-4ac
Δ = -422-4·21·(-63)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-84}{2*21}=\frac{-42}{42}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+84}{2*21}=\frac{126}{42}
=3
$