(2x+9)(3x+4)=0

Solution for (2x+9)(3x+4)=0 equation:

(2x+9)(3x+4)=0

We multiply parentheses ..

(+6x^2+8x+27x+36)=0

We get rid of parentheses

6x^2+8x+27x+36=0

We add all the numbers together, and all the variables

6x^2+35x+36=0

a = 6; b = 35; c = +36;
Δ = b2-4ac
Δ = 352-4·6·36
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-19}{2*6}=\frac{-54}{12}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+19}{2*6}=\frac{-16}{12}
=-1+1/3
$