2(x+5)(2x+9)=0

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

2(x+5)(2x+9)=0

We multiply parentheses ..

2(+2x^2+9x+10x+45)=0

We multiply parentheses

4x^2+18x+20x+90=0

We add all the numbers together, and all the variables

4x^2+38x+90=0

a = 4; b = 38; c = +90;
Δ = b2-4ac
Δ = 382-4·4·90
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2}{2*4}=\frac{-36}{8}
=-4+1/2
$