(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)(-1w+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+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
$