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

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

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

We multiply parentheses ..

(+2x^2+18x-4x-36)=0

We get rid of parentheses

2x^2+18x-4x-36=0

We add all the numbers together, and all the variables

2x^2+14x-36=0

a = 2; b = 14; c = -36;
Δ = b2-4ac
Δ = 142-4·2·(-36)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-22}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+22}{2*2}=\frac{8}{4}
=2
$