1/4w-1=5/5w

Solution for 1/4w-1=5/5w equation:

1/4w-1=5/5w

We move all terms to the left:

1/4w-1-(5/5w)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 5w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/4w-5/5w-1=0

We calculate fractions


5w/20w^2+(-20w)/20w^2-1=0

We multiply all the terms by the denominator


5w+(-20w)-1*20w^2=0

Wy multiply elements

-20w^2+5w+(-20w)=0

We get rid of parentheses

-20w^2+5w-20w=0

We add all the numbers together, and all the variables

-20w^2-15w=0

a = -20; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-20)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-20}=\frac{0}{-40}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-20}=\frac{30}{-40}
=-3/4
$