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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+4w^2-9w+8w-18)=0

We get rid of parentheses

4w^2-9w+8w-18=0

We add all the numbers together, and all the variables

4w^2-1w-18=0

a = 4; b = -1; c = -18;
Δ = b2-4ac
Δ = -12-4·4·(-18)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*4}=\frac{-16}{8}
=-2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*4}=\frac{18}{8}
=2+1/4
$