(7/2w+10)+4=-2/w+5

Solution for (7/2w+10)+4=-2/w+5 equation:

(7/2w+10)+4=-2/w+5

We move all terms to the left:

(7/2w+10)+4-(-2/w+5)=0


Domain of the equation: 2w+10)!=0

w∈R



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

w∈R


We get rid of parentheses

7/2w+2/w+10-5+4=0

We calculate fractions


7w/2w^2+4w/2w^2+10-5+4=0

We add all the numbers together, and all the variables

7w/2w^2+4w/2w^2+9=0

We multiply all the terms by the denominator


7w+4w+9*2w^2=0

We add all the numbers together, and all the variables

11w+9*2w^2=0

Wy multiply elements

18w^2+11w=0

a = 18; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·18·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*18}=\frac{-22}{36}
=-11/18
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*18}=\frac{0}{36}
=0
$