2w^2-4w=55

Solution for 2w^2-4w=55 equation:

2w^2-4w=55

We move all terms to the left:

2w^2-4w-(55)=0

a = 2; b = -4; c = -55;
Δ = b2-4ac
Δ = -42-4·2·(-55)
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{-(-4)-2\sqrt{114}}{2*2}=\frac{4-2\sqrt{114}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{114}}{2*2}=\frac{4+2\sqrt{114}}{4}
$