1/4w+3=5/4ww=

Solution for 1/4w+3=5/4ww= equation:

1/4w+3=5/4ww=

We move all terms to the left:

1/4w+3-(5/4ww)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 4ww)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

1/4w-(+5/4ww)+3=0

We get rid of parentheses

1/4w-5/4ww+3=0

We calculate fractions


4w/16w^2+(-20w)/16w^2+3=0

We multiply all the terms by the denominator


4w+(-20w)+3*16w^2=0

Wy multiply elements

48w^2+4w+(-20w)=0

We get rid of parentheses

48w^2+4w-20w=0

We add all the numbers together, and all the variables

48w^2-16w=0

a = 48; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·48·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*48}=\frac{0}{96}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*48}=\frac{32}{96}
=1/3
$