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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2w^2-6w-3w+9)-55=0

We get rid of parentheses

2w^2-6w-3w+9-55=0

We add all the numbers together, and all the variables

2w^2-9w-46=0

a = 2; b = -9; c = -46;
Δ = b2-4ac
Δ = -92-4·2·(-46)
Δ = 449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{449}}{2*2}=\frac{9-\sqrt{449}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{449}}{2*2}=\frac{9+\sqrt{449}}{4}
$