(3x+9)(8x+6)+(2x+5)(3x+9)=0

Solution for (3x+9)(8x+6)+(2x+5)(3x+9)=0 equation:

(3x+9)(8x+6)+(2x+5)(3x+9)=0

We multiply parentheses ..

(+24x^2+18x+72x+54)+(2x+5)(3x+9)=0

We get rid of parentheses

24x^2+18x+72x+(2x+5)(3x+9)+54=0

We multiply parentheses ..

24x^2+(+6x^2+18x+15x+45)+18x+72x+54=0

We add all the numbers together, and all the variables

24x^2+(+6x^2+18x+15x+45)+90x+54=0

We get rid of parentheses

24x^2+6x^2+18x+15x+90x+45+54=0

We add all the numbers together, and all the variables

30x^2+123x+99=0

a = 30; b = 123; c = +99;
Δ = b2-4ac
Δ = 1232-4·30·99
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(123)-57}{2*30}=\frac{-180}{60}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(123)+57}{2*30}=\frac{-66}{60}
=-1+1/10
$