w-9=3/4w

Solution for w-9=3/4w equation:

w-9=3/4w

We move all terms to the left:

w-9-(3/4w)=0


Domain of the equation: 4w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

w-3/4w-9=0

We multiply all the terms by the denominator


w*4w-9*4w-3=0

Wy multiply elements

4w^2-36w-3=0

a = 4; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·4·(-3)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{21}}{2*4}=\frac{36-8\sqrt{21}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{21}}{2*4}=\frac{36+8\sqrt{21}}{8}
$