1/4(w)+3/8(w)+1=12/8

Solution for 1/4(w)+3/8(w)+1=12/8 equation:

1/4(w)+3/8(w)+1=12/8

We move all terms to the left:

1/4(w)+3/8(w)+1-(12/8)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 8w!=0

w!=0/8

w!=0

w∈R


We add all the numbers together, and all the variables

1/4w+3/8w+1-(+12/8)=0

We get rid of parentheses

1/4w+3/8w+1-12/8=0

We calculate fractions


512w/2048w^2+12w/2048w^2+(-48w)/2048w^2+1=0

We multiply all the terms by the denominator


512w+12w+(-48w)+1*2048w^2=0

We add all the numbers together, and all the variables

524w+(-48w)+1*2048w^2=0

Wy multiply elements

2048w^2+524w+(-48w)=0

We get rid of parentheses

2048w^2+524w-48w=0

We add all the numbers together, and all the variables

2048w^2+476w=0

a = 2048; b = 476; c = 0;
Δ = b2-4ac
Δ = 4762-4·2048·0
Δ = 226576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{226576}=476$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(476)-476}{2*2048}=\frac{-952}{4096}
=-119/512
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(476)+476}{2*2048}=\frac{0}{4096}
=0
$