1/10x=6-3/5x

Solution for 1/10x=6-3/5x equation:

1/10x=6-3/5x

We move all terms to the left:

1/10x-(6-3/5x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/10x-(-3/5x+6)=0

We get rid of parentheses

1/10x+3/5x-6=0

We calculate fractions


5x/50x^2+30x/50x^2-6=0

We multiply all the terms by the denominator


5x+30x-6*50x^2=0

We add all the numbers together, and all the variables

35x-6*50x^2=0

Wy multiply elements

-300x^2+35x=0

a = -300; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-300)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-300}=\frac{-70}{-600}
=7/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-300}=\frac{0}{-600}
=0
$