(w/2-2)w=63^2

Solution for (w/2-2)w=63^2 equation:

(w/2-2)w=63^2

We move all terms to the left:

(w/2-2)w-(63^2)=0


Domain of the equation: 2-2)w!=0

We move all terms containing w to the left, all other terms to the right

-2)w!=-2

w!=-2/1

w!=-2

w∈R


We add all the numbers together, and all the variables

(w/2-2)w-3969=0

We multiply parentheses

w^2-2w-3969=0

a = 1; b = -2; c = -3969;
Δ = b2-4ac
Δ = -22-4·1·(-3969)
Δ = 15880
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:

$\sqrt{\Delta}=\sqrt{15880}=\sqrt{4*3970}=\sqrt{4}*\sqrt{3970}=2\sqrt{3970}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3970}}{2*1}=\frac{2-2\sqrt{3970}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3970}}{2*1}=\frac{2+2\sqrt{3970}}{2}
$