1/6x-4=3+3/10x

Solution for 1/6x-4=3+3/10x equation:

1/6x-4=3+3/10x

We move all terms to the left:

1/6x-4-(3+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+3)-4=0

We get rid of parentheses

1/6x-3/10x-3-4=0

We calculate fractions


10x/60x^2+(-18x)/60x^2-3-4=0

We add all the numbers together, and all the variables

10x/60x^2+(-18x)/60x^2-7=0

We multiply all the terms by the denominator


10x+(-18x)-7*60x^2=0

Wy multiply elements

-420x^2+10x+(-18x)=0

We get rid of parentheses

-420x^2+10x-18x=0

We add all the numbers together, and all the variables

-420x^2-8x=0

a = -420; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-420)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-420}=\frac{0}{-840}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-420}=\frac{16}{-840}
=-2/105
$