3w-1=1/4(12w)-+1

Solution for 3w-1=1/4(12w)-+1 equation:

3w-1=1/4(12w)-+1

We move all terms to the left:

3w-1-(1/4(12w)-+1)=0


Domain of the equation: 412w-+1)!=0

w∈R


We add all the numbers together, and all the variables

3w-(+1/412w)-1=0

We get rid of parentheses

3w-1/412w-1=0

We multiply all the terms by the denominator


3w*412w-1*412w-1=0

Wy multiply elements

1236w^2-412w-1=0

a = 1236; b = -412; c = -1;
Δ = b2-4ac
Δ = -4122-4·1236·(-1)
Δ = 174688
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:

$\sqrt{\Delta}=\sqrt{174688}=\sqrt{16*10918}=\sqrt{16}*\sqrt{10918}=4\sqrt{10918}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-412)-4\sqrt{10918}}{2*1236}=\frac{412-4\sqrt{10918}}{2472}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-412)+4\sqrt{10918}}{2*1236}=\frac{412+4\sqrt{10918}}{2472}
$