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

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

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

We multiply parentheses ..

5(+w^2-2w-9w+18)=0

We multiply parentheses

5w^2-10w-45w+90=0

We add all the numbers together, and all the variables

5w^2-55w+90=0

a = 5; b = -55; c = +90;
Δ = b2-4ac
Δ = -552-4·5·90
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-35}{2*5}=\frac{20}{10}
=2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+35}{2*5}=\frac{90}{10}
=9
$