(w-5)(5w-12)=0

Solution for (w-5)(5w-12)=0 equation:

(w-5)(5w-12)=0

We multiply parentheses ..

(+5w^2-12w-25w+60)=0

We get rid of parentheses

5w^2-12w-25w+60=0

We add all the numbers together, and all the variables

5w^2-37w+60=0

a = 5; b = -37; c = +60;
Δ = b2-4ac
Δ = -372-4·5·60
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-13}{2*5}=\frac{24}{10}
=2+2/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+13}{2*5}=\frac{50}{10}
=5
$