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

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

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

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 5w+1)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


5w/10w^2+(-6w)/10w^2-1-4=0

We add all the numbers together, and all the variables

5w/10w^2+(-6w)/10w^2-5=0

We multiply all the terms by the denominator


5w+(-6w)-5*10w^2=0

Wy multiply elements

-50w^2+5w+(-6w)=0

We get rid of parentheses

-50w^2+5w-6w=0

We add all the numbers together, and all the variables

-50w^2-1w=0

a = -50; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-50)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-50}=\frac{0}{-100}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-50}=\frac{2}{-100}
=-1/50
$