4/3w+2w=28

Solution for 4/3w+2w=28 equation:

4/3w+2w=28

We move all terms to the left:

4/3w+2w-(28)=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+4/3w-28=0

We multiply all the terms by the denominator


2w*3w-28*3w+4=0

Wy multiply elements

6w^2-84w+4=0

a = 6; b = -84; c = +4;
Δ = b2-4ac
Δ = -842-4·6·4
Δ = 6960
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:

$\sqrt{\Delta}=\sqrt{6960}=\sqrt{16*435}=\sqrt{16}*\sqrt{435}=4\sqrt{435}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{435}}{2*6}=\frac{84-4\sqrt{435}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{435}}{2*6}=\frac{84+4\sqrt{435}}{12}
$