1/x=10/3x+10

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

1/x=10/3x+10

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+10)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


3x+(-10x)-10*3x^2=0

Wy multiply elements

-30x^2+3x+(-10x)=0

We get rid of parentheses

-30x^2+3x-10x=0

We add all the numbers together, and all the variables

-30x^2-7x=0

a = -30; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-30)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-30}=\frac{0}{-60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-30}=\frac{14}{-60}
=-7/30
$