1/4w+8=1/2w-6

Solution for 1/4w+8=1/2w-6 equation:

1/4w+8=1/2w-6

We move all terms to the left:

1/4w+8-(1/2w-6)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 2w-6)!=0

w∈R


We get rid of parentheses

1/4w-1/2w+6+8=0

We calculate fractions


2w/8w^2+(-4w)/8w^2+6+8=0

We add all the numbers together, and all the variables

2w/8w^2+(-4w)/8w^2+14=0

We multiply all the terms by the denominator


2w+(-4w)+14*8w^2=0

Wy multiply elements

112w^2+2w+(-4w)=0

We get rid of parentheses

112w^2+2w-4w=0

We add all the numbers together, and all the variables

112w^2-2w=0

a = 112; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·112·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*112}=\frac{0}{224}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*112}=\frac{4}{224}
=1/56
$