6/5w+9/w=1

Solution for 6/5w+9/w=1 equation:

6/5w+9/w=1

We move all terms to the left:

6/5w+9/w-(1)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: w!=0

w∈R


We calculate fractions


6w/5w^2+45w/5w^2-1=0

We multiply all the terms by the denominator


6w+45w-1*5w^2=0

We add all the numbers together, and all the variables

51w-1*5w^2=0

Wy multiply elements

-5w^2+51w=0

a = -5; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-5)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-5}=\frac{-102}{-10}
=10+1/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-5}=\frac{0}{-10}
=0
$