(6x-7)(-3x-9)=0

Solution for (6x-7)(-3x-9)=0 equation:

(6x-7)(-3x-9)=0

We multiply parentheses ..

(-18x^2-54x+21x+63)=0

We get rid of parentheses

-18x^2-54x+21x+63=0

We add all the numbers together, and all the variables

-18x^2-33x+63=0

a = -18; b = -33; c = +63;
Δ = b2-4ac
Δ = -332-4·(-18)·63
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-75}{2*-18}=\frac{-42}{-36}
=1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+75}{2*-18}=\frac{108}{-36}
=-3
$