(2w-3)(9+w)=0

Solution for (2w-3)(9+w)=0 equation:

(2w-3)(9+w)=0

We add all the numbers together, and all the variables

(2w-3)(w+9)=0

We multiply parentheses ..

(+2w^2+18w-3w-27)=0

We get rid of parentheses

2w^2+18w-3w-27=0

We add all the numbers together, and all the variables

2w^2+15w-27=0

a = 2; b = 15; c = -27;
Δ = b2-4ac
Δ = 152-4·2·(-27)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*2}=\frac{-36}{4}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*2}=\frac{6}{4}
=1+1/2
$