126=(46-2w)w

Solution for 126=(46-2w)w equation:

126=(46-2w)w

We move all terms to the left:

126-((46-2w)w)=0

We add all the numbers together, and all the variables

-((-2w+46)w)+126=0


We calculate terms in parentheses: -((-2w+46)w), so:

(-2w+46)w

We multiply parentheses

-2w^2+46w

Back to the equation:

-(-2w^2+46w)


We get rid of parentheses

2w^2-46w+126=0

a = 2; b = -46; c = +126;
Δ = b2-4ac
Δ = -462-4·2·126
Δ = 1108
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:

$\sqrt{\Delta}=\sqrt{1108}=\sqrt{4*277}=\sqrt{4}*\sqrt{277}=2\sqrt{277}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{277}}{2*2}=\frac{46-2\sqrt{277}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{277}}{2*2}=\frac{46+2\sqrt{277}}{4}
$