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

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

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

We multiply parentheses ..

(+3x^2-21x+9x-63)=0

We get rid of parentheses

3x^2-21x+9x-63=0

We add all the numbers together, and all the variables

3x^2-12x-63=0

a = 3; b = -12; c = -63;
Δ = b2-4ac
Δ = -122-4·3·(-63)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-30}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+30}{2*3}=\frac{42}{6}
=7
$