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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+4w^2-10w-6w+15)-55=0

We get rid of parentheses

4w^2-10w-6w+15-55=0

We add all the numbers together, and all the variables

4w^2-16w-40=0

a = 4; b = -16; c = -40;
Δ = b2-4ac
Δ = -162-4·4·(-40)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{14}}{2*4}=\frac{16-8\sqrt{14}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{14}}{2*4}=\frac{16+8\sqrt{14}}{8}
$