14-1/w=3/4w-21

Solution for 14-1/w=3/4w-21 equation:

14-1/w=3/4w-21

We move all terms to the left:

14-1/w-(3/4w-21)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: 4w-21)!=0

w∈R


We get rid of parentheses

-1/w-3/4w+21+14=0

We calculate fractions


(-4w)/4w^2+(-3w)/4w^2+21+14=0

We add all the numbers together, and all the variables

(-4w)/4w^2+(-3w)/4w^2+35=0

We multiply all the terms by the denominator


(-4w)+(-3w)+35*4w^2=0

Wy multiply elements

140w^2+(-4w)+(-3w)=0

We get rid of parentheses

140w^2-4w-3w=0

We add all the numbers together, and all the variables

140w^2-7w=0

a = 140; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·140·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*140}=\frac{0}{280}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*140}=\frac{14}{280}
=1/20
$