3/5w-1/2=-3/10w

Solution for 3/5w-1/2=-3/10w equation:

3/5w-1/2=-3/10w

We move all terms to the left:

3/5w-1/2-(-3/10w)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 10w)!=0

w!=0/1

w!=0

w∈R


We get rid of parentheses

3/5w+3/10w-1/2=0

We calculate fractions


(-50w^2)/200w^2+120w/200w^2+60w/200w^2=0

We multiply all the terms by the denominator


(-50w^2)+120w+60w=0

We add all the numbers together, and all the variables

(-50w^2)+180w=0

We get rid of parentheses

-50w^2+180w=0

a = -50; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-50)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-50}=\frac{-360}{-100}
=3+3/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-50}=\frac{0}{-100}
=0
$