(3x-9)(2x-7)=0

Solution for (3x-9)(2x-7)=0 equation:

(3x-9)(2x-7)=0

We multiply parentheses ..

(+6x^2-21x-18x+63)=0

We get rid of parentheses

6x^2-21x-18x+63=0

We add all the numbers together, and all the variables

6x^2-39x+63=0

a = 6; b = -39; c = +63;
Δ = b2-4ac
Δ = -392-4·6·63
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3}{2*6}=\frac{36}{12}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3}{2*6}=\frac{42}{12}
=3+1/2
$