5(w-3)(-w+8)=0

Solution for 5(w-3)(-w+8)=0 equation:

5(w-3)(-w+8)=0

We add all the numbers together, and all the variables

5(w-3)(-1w+8)=0

We multiply parentheses ..

5(-1w^2+8w+3w-24)=0

We multiply parentheses

-5w^2+40w+15w-120=0

We add all the numbers together, and all the variables

-5w^2+55w-120=0

a = -5; b = 55; c = -120;
Δ = b2-4ac
Δ = 552-4·(-5)·(-120)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-25}{2*-5}=\frac{-80}{-10}
=+8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+25}{2*-5}=\frac{-30}{-10}
=+3
$