1/5x-13/30=3/2x

Solution for 1/5x-13/30=3/2x equation:

1/5x-13/30=3/2x

We move all terms to the left:

1/5x-13/30-(3/2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(+3/2x)-13/30=0

We get rid of parentheses

1/5x-3/2x-13/30=0

We calculate fractions


(-260x^2)/900x^2+180x/900x^2+(-1350x)/900x^2=0

We multiply all the terms by the denominator


(-260x^2)+180x+(-1350x)=0

We get rid of parentheses

-260x^2+180x-1350x=0

We add all the numbers together, and all the variables

-260x^2-1170x=0

a = -260; b = -1170; c = 0;
Δ = b2-4ac
Δ = -11702-4·(-260)·0
Δ = 1368900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1368900}=1170$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1170)-1170}{2*-260}=\frac{0}{-520}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1170)+1170}{2*-260}=\frac{2340}{-520}
=-4+1/2
$