460=2(1w+30)2w

Solution for 460=2(1w+30)2w equation:

460=2(1w+30)2w

We move all terms to the left:

460-(2(1w+30)2w)=0

We add all the numbers together, and all the variables

-(2(w+30)2w)+460=0


We calculate terms in parentheses: -(2(w+30)2w), so:

2(w+30)2w

We multiply parentheses

4w^2+120w

Back to the equation:

-(4w^2+120w)


We get rid of parentheses

-4w^2-120w+460=0

a = -4; b = -120; c = +460;
Δ = b2-4ac
Δ = -1202-4·(-4)·460
Δ = 21760
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:

$\sqrt{\Delta}=\sqrt{21760}=\sqrt{256*85}=\sqrt{256}*\sqrt{85}=16\sqrt{85}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-16\sqrt{85}}{2*-4}=\frac{120-16\sqrt{85}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+16\sqrt{85}}{2*-4}=\frac{120+16\sqrt{85}}{-8}
$