7/4w+16+1=-1/w+4

Solution for 7/4w+16+1=-1/w+4 equation:

7/4w+16+1=-1/w+4

We move all terms to the left:

7/4w+16+1-(-1/w+4)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: w+4)!=0

w∈R


We add all the numbers together, and all the variables

7/4w-(-1/w+4)+17=0

We get rid of parentheses

7/4w+1/w-4+17=0

We calculate fractions


7w/4w^2+4w/4w^2-4+17=0

We add all the numbers together, and all the variables

7w/4w^2+4w/4w^2+13=0

We multiply all the terms by the denominator


7w+4w+13*4w^2=0

We add all the numbers together, and all the variables

11w+13*4w^2=0

Wy multiply elements

52w^2+11w=0

a = 52; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·52·0
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*52}=\frac{-22}{104}
=-11/52
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*52}=\frac{0}{104}
=0
$