(6x-7)(-3x-9)+18x=0

Solution for (6x-7)(-3x-9)+18x=0 equation:

(6x-7)(-3x-9)+18x=0

We add all the numbers together, and all the variables

18x+(6x-7)(-3x-9)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-18x^2-15x+63=0

a = -18; b = -15; c = +63;
Δ = b2-4ac
Δ = -152-4·(-18)·63
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-69}{2*-18}=\frac{-54}{-36}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+69}{2*-18}=\frac{84}{-36}
=-2+1/3
$