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

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

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

We multiply parentheses ..

(+3x^2-27x+7x-63)=0

We get rid of parentheses

3x^2-27x+7x-63=0

We add all the numbers together, and all the variables

3x^2-20x-63=0

a = 3; b = -20; c = -63;
Δ = b2-4ac
Δ = -202-4·3·(-63)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-34}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+34}{2*3}=\frac{54}{6}
=9
$