2/3w+2/3w+w+w=380

Solution for 2/3w+2/3w+w+w=380 equation:

2/3w+2/3w+w+w=380

We move all terms to the left:

2/3w+2/3w+w+w-(380)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We add all the numbers together, and all the variables

2w+2/3w+2/3w-380=0

We multiply all the terms by the denominator


2w*3w-380*3w+2+2=0

We add all the numbers together, and all the variables

2w*3w-380*3w+4=0

Wy multiply elements

6w^2-1140w+4=0

a = 6; b = -1140; c = +4;
Δ = b2-4ac
Δ = -11402-4·6·4
Δ = 1299504
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:

$\sqrt{\Delta}=\sqrt{1299504}=\sqrt{16*81219}=\sqrt{16}*\sqrt{81219}=4\sqrt{81219}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1140)-4\sqrt{81219}}{2*6}=\frac{1140-4\sqrt{81219}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1140)+4\sqrt{81219}}{2*6}=\frac{1140+4\sqrt{81219}}{12}
$