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

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

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

We multiply parentheses ..

(+8x^2+18x+12x+27)=0

We get rid of parentheses

8x^2+18x+12x+27=0

We add all the numbers together, and all the variables

8x^2+30x+27=0

a = 8; b = 30; c = +27;
Δ = b2-4ac
Δ = 302-4·8·27
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6}{2*8}=\frac{-36}{16}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6}{2*8}=\frac{-24}{16}
=-1+1/2
$