-1/2+-3/5x=1/6x+3

Solution for -1/2+-3/5x=1/6x+3 equation:

-1/2+-3/5x=1/6x+3

We move all terms to the left:

-1/2+-3/5x-(1/6x+3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x+3)!=0

x∈R


We add all the numbers together, and all the variables

-3/5x-(1/6x+3)-1/2=0

We get rid of parentheses

-3/5x-1/6x-3-1/2=0

We calculate fractions


(-180x^2)/120x^2+(-72x)/120x^2+(-20x)/120x^2-3=0

We multiply all the terms by the denominator


(-180x^2)+(-72x)+(-20x)-3*120x^2=0

Wy multiply elements

(-180x^2)-360x^2+(-72x)+(-20x)=0

We get rid of parentheses

-180x^2-360x^2-72x-20x=0

We add all the numbers together, and all the variables

-540x^2-92x=0

a = -540; b = -92; c = 0;
Δ = b2-4ac
Δ = -922-4·(-540)·0
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-92}{2*-540}=\frac{0}{-1080}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+92}{2*-540}=\frac{184}{-1080}
=-23/135
$