6x=30/x

Solution for 6x=30/x equation:

6x=30/x

We move all terms to the left:

6x-(30/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+30/x)=0

We get rid of parentheses

6x-30/x=0

We multiply all the terms by the denominator


6x*x-30=0

Wy multiply elements

6x^2-30=0

a = 6; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·6·(-30)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*6}=\frac{0-12\sqrt{5}}{12}
=-\frac{12\sqrt{5}}{12}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*6}=\frac{0+12\sqrt{5}}{12}
=\frac{12\sqrt{5}}{12}
=\sqrt{5}
$