3/w-5+2/w+5*w-5=1/w+5

Solution for 3/w-5+2/w+5*w-5=1/w+5 equation:

3/w-5+2/w+5w-5=1/w+5

We move all terms to the left:

3/w-5+2/w+5w-5-(1/w+5)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: w+5)!=0

w∈R


We add all the numbers together, and all the variables

5w+3/w+2/w-(1/w+5)-10=0

We get rid of parentheses

5w+3/w+2/w-1/w-5-10=0

We multiply all the terms by the denominator


5w*w-5*w-10*w+3+2-1=0

We add all the numbers together, and all the variables

-15w+5w*w+4=0

Wy multiply elements

5w^2-15w+4=0

a = 5; b = -15; c = +4;
Δ = b2-4ac
Δ = -152-4·5·4
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{145}}{2*5}=\frac{15-\sqrt{145}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{145}}{2*5}=\frac{15+\sqrt{145}}{10}
$