-4/w-5=-7/4w-20+1

Solution for -4/w-5=-7/4w-20+1 equation:

-4/w-5=-7/4w-20+1

We move all terms to the left:

-4/w-5-(-7/4w-20+1)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: 4w-20+1)!=0

We move all terms containing w to the left, all other terms to the right

4w+1)!=20

w∈R


We add all the numbers together, and all the variables

-4/w-(-7/4w-19)-5=0

We get rid of parentheses

-4/w+7/4w+19-5=0

We calculate fractions


(-16w)/4w^2+7w/4w^2+19-5=0

We add all the numbers together, and all the variables

(-16w)/4w^2+7w/4w^2+14=0

We multiply all the terms by the denominator


(-16w)+7w+14*4w^2=0

We add all the numbers together, and all the variables

7w+(-16w)+14*4w^2=0

Wy multiply elements

56w^2+7w+(-16w)=0

We get rid of parentheses

56w^2+7w-16w=0

We add all the numbers together, and all the variables

56w^2-9w=0

a = 56; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·56·0
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*56}=\frac{0}{112}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*56}=\frac{18}{112}
=9/56
$