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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2w^2-10w-5w+25)-55=0

We get rid of parentheses

2w^2-10w-5w+25-55=0

We add all the numbers together, and all the variables

2w^2-15w-30=0

a = 2; b = -15; c = -30;
Δ = b2-4ac
Δ = -152-4·2·(-30)
Δ = 465
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{-(-15)-\sqrt{465}}{2*2}=\frac{15-\sqrt{465}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{465}}{2*2}=\frac{15+\sqrt{465}}{4}
$