(9+w)(2w-5)=0

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

(9+w)(2w-5)=0

We add all the numbers together, and all the variables

(w+9)(2w-5)=0

We multiply parentheses ..

(+2w^2-5w+18w-45)=0

We get rid of parentheses

2w^2-5w+18w-45=0

We add all the numbers together, and all the variables

2w^2+13w-45=0

a = 2; b = 13; c = -45;
Δ = b2-4ac
Δ = 132-4·2·(-45)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-23}{2*2}=\frac{-36}{4}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+23}{2*2}=\frac{10}{4}
=2+1/2
$