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

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

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

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

6x/10x^2+(-5x)/10x^2-8=0

We multiply all the terms by the denominator


6x+(-5x)-8*10x^2=0

Wy multiply elements

-80x^2+6x+(-5x)=0

We get rid of parentheses

-80x^2+6x-5x=0

We add all the numbers together, and all the variables

-80x^2+x=0

a = -80; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-80)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-80}=\frac{-2}{-160}
=1/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-80}=\frac{0}{-160}
=0
$