2(w-3)(w-5)=55

Solution for 2(w-3)(w-5)=55 equation:

2(w-3)(w-5)=55

We move all terms to the left:

2(w-3)(w-5)-(55)=0

We multiply parentheses ..

2(+w^2-5w-3w+15)-55=0

We multiply parentheses

2w^2-10w-6w+30-55=0

We add all the numbers together, and all the variables

2w^2-16w-25=0

a = 2; b = -16; c = -25;
Δ = b2-4ac
Δ = -162-4·2·(-25)
Δ = 456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{114}}{2*2}=\frac{16-2\sqrt{114}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{114}}{2*2}=\frac{16+2\sqrt{114}}{4}
$