1/7w-1/2=1/14w

Solution for 1/7w-1/2=1/14w equation:

1/7w-1/2=1/14w

We move all terms to the left:

1/7w-1/2-(1/14w)=0


Domain of the equation: 7w!=0

w!=0/7

w!=0

w∈R



Domain of the equation: 14w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

1/7w-(+1/14w)-1/2=0

We get rid of parentheses

1/7w-1/14w-1/2=0

We calculate fractions


(-98w^2)/392w^2+56w/392w^2+(-28w)/392w^2=0

We multiply all the terms by the denominator


(-98w^2)+56w+(-28w)=0

We get rid of parentheses

-98w^2+56w-28w=0

We add all the numbers together, and all the variables

-98w^2+28w=0

a = -98; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-98)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-98}=\frac{-56}{-196}
=2/7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-98}=\frac{0}{-196}
=0
$