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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2w^2+23w+45=0

a = 2; b = 23; c = +45;
Δ = b2-4ac
Δ = 232-4·2·45
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-13}{2*2}=\frac{-36}{4}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+13}{2*2}=\frac{-10}{4}
=-2+1/2
$