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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-1x^2)/3x^2+15x/3x^2+1+10=0

We add all the numbers together, and all the variables

(-1x^2)/3x^2+15x/3x^2+11=0

We multiply all the terms by the denominator


(-1x^2)+15x+11*3x^2=0

Wy multiply elements

(-1x^2)+33x^2+15x=0

We get rid of parentheses

-1x^2+33x^2+15x=0

We add all the numbers together, and all the variables

32x^2+15x=0

a = 32; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·32·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*32}=\frac{-30}{64}
=-15/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*32}=\frac{0}{64}
=0
$