7/8w+2=5/4w+1

Solution for 7/8w+2=5/4w+1 equation:

7/8w+2=5/4w+1

We move all terms to the left:

7/8w+2-(5/4w+1)=0


Domain of the equation: 8w!=0

w!=0/8

w!=0

w∈R



Domain of the equation: 4w+1)!=0

w∈R


We get rid of parentheses

7/8w-5/4w-1+2=0

We calculate fractions


28w/32w^2+(-40w)/32w^2-1+2=0

We add all the numbers together, and all the variables

28w/32w^2+(-40w)/32w^2+1=0

We multiply all the terms by the denominator


28w+(-40w)+1*32w^2=0

Wy multiply elements

32w^2+28w+(-40w)=0

We get rid of parentheses

32w^2+28w-40w=0

We add all the numbers together, and all the variables

32w^2-12w=0

a = 32; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·32·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*32}=\frac{0}{64}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*32}=\frac{24}{64}
=3/8
$