3w+6=9-1/4w

Solution for 3w+6=9-1/4w equation:

3w+6=9-1/4w

We move all terms to the left:

3w+6-(9-1/4w)=0


Domain of the equation: 4w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

3w-(-1/4w+9)+6=0

We get rid of parentheses

3w+1/4w-9+6=0

We multiply all the terms by the denominator


3w*4w-9*4w+6*4w+1=0

Wy multiply elements

12w^2-36w+24w+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 = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{6}}{2*12}=\frac{12-4\sqrt{6}}{24}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{6}}{2*12}=\frac{12+4\sqrt{6}}{24}
$