1/4w+2=2w-1+w

Solution for 1/4w+2=2w-1+w equation:

1/4w+2=2w-1+w

We move all terms to the left:

1/4w+2-(2w-1+w)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We add all the numbers together, and all the variables

1/4w-(3w-1)+2=0

We get rid of parentheses

1/4w-3w+1+2=0

We multiply all the terms by the denominator


-3w*4w+1*4w+2*4w+1=0

Wy multiply elements

-12w^2+4w+8w+1=0

We add all the numbers together, and all the variables

-12w^2+12w+1=0

a = -12; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-12)·1
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{3}}{2*-12}=\frac{-12-8\sqrt{3}}{-24}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{3}}{2*-12}=\frac{-12+8\sqrt{3}}{-24}
$