w^2-2w=455

Solution for w^2-2w=455 equation:

w^2-2w=455

We move all terms to the left:

w^2-2w-(455)=0

a = 1; b = -2; c = -455;
Δ = b2-4ac
Δ = -22-4·1·(-455)
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{114}}{2*1}=\frac{2-4\sqrt{114}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{114}}{2*1}=\frac{2+4\sqrt{114}}{2}
$