7/4w+12+1=-3/w+3

Solution for 7/4w+12+1=-3/w+3 equation:

7/4w+12+1=-3/w+3

We move all terms to the left:

7/4w+12+1-(-3/w+3)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: w+3)!=0

w∈R


We add all the numbers together, and all the variables

7/4w-(-3/w+3)+13=0

We get rid of parentheses

7/4w+3/w-3+13=0

We calculate fractions


7w/4w^2+12w/4w^2-3+13=0

We add all the numbers together, and all the variables

7w/4w^2+12w/4w^2+10=0

We multiply all the terms by the denominator


7w+12w+10*4w^2=0

We add all the numbers together, and all the variables

19w+10*4w^2=0

Wy multiply elements

40w^2+19w=0

a = 40; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·40·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*40}=\frac{-38}{80}
=-19/40
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*40}=\frac{0}{80}
=0
$