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

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

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

We multiply parentheses ..

(+2x^2+8x-9x-36)=0

We get rid of parentheses

2x^2+8x-9x-36=0

We add all the numbers together, and all the variables

2x^2-1x-36=0

a = 2; b = -1; c = -36;
Δ = b2-4ac
Δ = -12-4·2·(-36)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*2}=\frac{18}{4}
=4+1/2
$