-3/5x+1/2=3/10x

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

-3/5x+1/2=3/10x

We move all terms to the left:

-3/5x+1/2-(3/10x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/5x-(+3/10x)+1/2=0

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We get rid of parentheses

50x^2-120x-60x=0

We add all the numbers together, and all the variables

50x^2-180x=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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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