(3/x)-10=6x

Solution for (3/x)-10=6x equation:

(3/x)-10=6x

We move all terms to the left:

(3/x)-10-(6x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-6x+3/x-10=0

We multiply all the terms by the denominator


-6x*x-10*x+3=0

We add all the numbers together, and all the variables

-10x-6x*x+3=0

Wy multiply elements

-6x^2-10x+3=0

a = -6; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·(-6)·3
Δ = 172
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{43}}{2*-6}=\frac{10-2\sqrt{43}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{43}}{2*-6}=\frac{10+2\sqrt{43}}{-12}
$