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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

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

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

We get rid of parentheses

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

We calculate fractions


180x^2/1500x^2+250x/1500x^2+450x/1500x^2-1=0

We multiply all the terms by the denominator


180x^2+250x+450x-1*1500x^2=0

We add all the numbers together, and all the variables

180x^2+700x-1*1500x^2=0

Wy multiply elements

180x^2-1500x^2+700x=0

We add all the numbers together, and all the variables

-1320x^2+700x=0

a = -1320; b = 700; c = 0;
Δ = b2-4ac
Δ = 7002-4·(-1320)·0
Δ = 490000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{490000}=700$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700)-700}{2*-1320}=\frac{-1400}{-2640}
=35/66
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700)+700}{2*-1320}=\frac{0}{-2640}
=0
$