-1/w+3=-5/4w+12+2

Solution for -1/w+3=-5/4w+12+2 equation:

-1/w+3=-5/4w+12+2

We move all terms to the left:

-1/w+3-(-5/4w+12+2)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: 4w+12+2)!=0

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

4w+2)!=-12

w∈R


We add all the numbers together, and all the variables

-1/w-(-5/4w+14)+3=0

We get rid of parentheses

-1/w+5/4w-14+3=0

We calculate fractions


(-4w)/4w^2+5w/4w^2-14+3=0

We add all the numbers together, and all the variables

(-4w)/4w^2+5w/4w^2-11=0

We multiply all the terms by the denominator


(-4w)+5w-11*4w^2=0

We add all the numbers together, and all the variables

5w+(-4w)-11*4w^2=0

Wy multiply elements

-44w^2+5w+(-4w)=0

We get rid of parentheses

-44w^2+5w-4w=0

We add all the numbers together, and all the variables

-44w^2+w=0

a = -44; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-44)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-44}=\frac{-2}{-88}
=1/44
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-44}=\frac{0}{-88}
=0
$