(w-1)(2w-5)=0

Solution for (w-1)(2w-5)=0 equation:

(w-1)(2w-5)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2w^2-7w+5=0

a = 2; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·2·5
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*2}=\frac{4}{4}
=1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*2}=\frac{10}{4}
=2+1/2
$