3/x-13=10x

Solution for 3/x-13=10x equation:

3/x-13=10x

We move all terms to the left:

3/x-13-(10x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-10x+3/x-13=0

We multiply all the terms by the denominator


-10x*x-13*x+3=0

We add all the numbers together, and all the variables

-13x-10x*x+3=0

Wy multiply elements

-10x^2-13x+3=0

a = -10; b = -13; c = +3;
Δ = b2-4ac
Δ = -132-4·(-10)·3
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*-10}=\frac{-4}{-20}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*-10}=\frac{30}{-20}
=-1+1/2
$