5/2w+10+2=-2/w+5

Solution for 5/2w+10+2=-2/w+5 equation:

5/2w+10+2=-2/w+5

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



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

w∈R


We add all the numbers together, and all the variables

5/2w-(-2/w+5)+12=0

We get rid of parentheses

5/2w+2/w-5+12=0

We calculate fractions


5w/2w^2+4w/2w^2-5+12=0

We add all the numbers together, and all the variables

5w/2w^2+4w/2w^2+7=0

We multiply all the terms by the denominator


5w+4w+7*2w^2=0

We add all the numbers together, and all the variables

9w+7*2w^2=0

Wy multiply elements

14w^2+9w=0

a = 14; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·14·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*14}=\frac{-18}{28}
=-9/14
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*14}=\frac{0}{28}
=0
$