3/5w-3/4=-1/2w+1

Solution for 3/5w-3/4=-1/2w+1 equation:

3/5w-3/4=-1/2w+1

We move all terms to the left:

3/5w-3/4-(-1/2w+1)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 2w+1)!=0

w∈R


We get rid of parentheses

3/5w+1/2w-1-3/4=0

We calculate fractions


(-60w^2)/160w^2+96w/160w^2+80w/160w^2-1=0

We multiply all the terms by the denominator


(-60w^2)+96w+80w-1*160w^2=0

We add all the numbers together, and all the variables

(-60w^2)+176w-1*160w^2=0

Wy multiply elements

(-60w^2)-160w^2+176w=0

We get rid of parentheses

-60w^2-160w^2+176w=0

We add all the numbers together, and all the variables

-220w^2+176w=0

a = -220; b = 176; c = 0;
Δ = b2-4ac
Δ = 1762-4·(-220)·0
Δ = 30976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30976}=176$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176)-176}{2*-220}=\frac{-352}{-440}
=4/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176)+176}{2*-220}=\frac{0}{-440}
=0
$