(5w+6)(9-w)=0

Solution for (5w+6)(9-w)=0 equation:

(5w+6)(9-w)=0

We add all the numbers together, and all the variables

(5w+6)(-1w+9)=0

We multiply parentheses ..

(-5w^2+45w-6w+54)=0

We get rid of parentheses

-5w^2+45w-6w+54=0

We add all the numbers together, and all the variables

-5w^2+39w+54=0

a = -5; b = 39; c = +54;
Δ = b2-4ac
Δ = 392-4·(-5)·54
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-51}{2*-5}=\frac{-90}{-10}
=+9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+51}{2*-5}=\frac{12}{-10}
=-1+1/5
$