7/5w+30+1=-5/w+6

Solution for 7/5w+30+1=-5/w+6 equation:

7/5w+30+1=-5/w+6

We move all terms to the left:

7/5w+30+1-(-5/w+6)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: w+6)!=0

w∈R


We add all the numbers together, and all the variables

7/5w-(-5/w+6)+31=0

We get rid of parentheses

7/5w+5/w-6+31=0

We calculate fractions


7w/5w^2+25w/5w^2-6+31=0

We add all the numbers together, and all the variables

7w/5w^2+25w/5w^2+25=0

We multiply all the terms by the denominator


7w+25w+25*5w^2=0

We add all the numbers together, and all the variables

32w+25*5w^2=0

Wy multiply elements

125w^2+32w=0

a = 125; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·125·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*125}=\frac{-64}{250}
=-32/125
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*125}=\frac{0}{250}
=0
$