1/3x=6/5x+10

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

1/3x=6/5x+10

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+10)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


5x/15x^2+(-18x)/15x^2-10=0

We multiply all the terms by the denominator


5x+(-18x)-10*15x^2=0

Wy multiply elements

-150x^2+5x+(-18x)=0

We get rid of parentheses

-150x^2+5x-18x=0

We add all the numbers together, and all the variables

-150x^2-13x=0

a = -150; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-150)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*-150}=\frac{0}{-300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-150}=\frac{26}{-300}
=-13/150
$