14-1/8w=3/4w-20

Solution for 14-1/8w=3/4w-20 equation:

14-1/8w=3/4w-20

We move all terms to the left:

14-1/8w-(3/4w-20)=0


Domain of the equation: 8w!=0

w!=0/8

w!=0

w∈R



Domain of the equation: 4w-20)!=0

w∈R


We get rid of parentheses

-1/8w-3/4w+20+14=0

We calculate fractions


(-4w)/32w^2+(-24w)/32w^2+20+14=0

We add all the numbers together, and all the variables

(-4w)/32w^2+(-24w)/32w^2+34=0

We multiply all the terms by the denominator


(-4w)+(-24w)+34*32w^2=0

Wy multiply elements

1088w^2+(-4w)+(-24w)=0

We get rid of parentheses

1088w^2-4w-24w=0

We add all the numbers together, and all the variables

1088w^2-28w=0

a = 1088; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·1088·0
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*1088}=\frac{0}{2176}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*1088}=\frac{56}{2176}
=7/272
$