286^2=(2w-4)w

Solution for 286^2=(2w-4)w equation:

286^2=(2w-4)w

We move all terms to the left:

286^2-((2w-4)w)=0

We add all the numbers together, and all the variables

-((2w-4)w)+81796=0


We calculate terms in parentheses: -((2w-4)w), so:

(2w-4)w

We multiply parentheses

2w^2-4w

Back to the equation:

-(2w^2-4w)


We get rid of parentheses

-2w^2+4w+81796=0

a = -2; b = 4; c = +81796;
Δ = b2-4ac
Δ = 42-4·(-2)·81796
Δ = 654384
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:

$\sqrt{\Delta}=\sqrt{654384}=\sqrt{16*40899}=\sqrt{16}*\sqrt{40899}=4\sqrt{40899}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{40899}}{2*-2}=\frac{-4-4\sqrt{40899}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{40899}}{2*-2}=\frac{-4+4\sqrt{40899}}{-4}
$