(6x+5)(3x-9)=0

Solution for (6x+5)(3x-9)=0 equation:

(6x+5)(3x-9)=0

We multiply parentheses ..

(+18x^2-54x+15x-45)=0

We get rid of parentheses

18x^2-54x+15x-45=0

We add all the numbers together, and all the variables

18x^2-39x-45=0

a = 18; b = -39; c = -45;
Δ = b2-4ac
Δ = -392-4·18·(-45)
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{-(-39)-69}{2*18}=\frac{-30}{36}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+69}{2*18}=\frac{108}{36}
=3
$