9/2w+6/w=1

Solution for 9/2w+6/w=1 equation:

9/2w+6/w=1

We move all terms to the left:

9/2w+6/w-(1)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: w!=0

w∈R


We calculate fractions


9w/2w^2+12w/2w^2-1=0

We multiply all the terms by the denominator


9w+12w-1*2w^2=0

We add all the numbers together, and all the variables

21w-1*2w^2=0

Wy multiply elements

-2w^2+21w=0

a = -2; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-2)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-2}=\frac{-42}{-4}
=10+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-2}=\frac{0}{-4}
=0
$