7/8w=3/4w+2

Solution for 7/8w=3/4w+2 equation:

7/8w=3/4w+2

We move all terms to the left:

7/8w-(3/4w+2)=0


Domain of the equation: 8w!=0

w!=0/8

w!=0

w∈R



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

w∈R


We get rid of parentheses

7/8w-3/4w-2=0

We calculate fractions


28w/32w^2+(-24w)/32w^2-2=0

We multiply all the terms by the denominator


28w+(-24w)-2*32w^2=0

Wy multiply elements

-64w^2+28w+(-24w)=0

We get rid of parentheses

-64w^2+28w-24w=0

We add all the numbers together, and all the variables

-64w^2+4w=0

a = -64; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-64)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-64}=\frac{-8}{-128}
=1/16
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-64}=\frac{0}{-128}
=0
$