60x=731/3x

Solution for 60x=731/3x equation:

60x=731/3x

We move all terms to the left:

60x-(731/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

60x-(+731/3x)=0

We get rid of parentheses

60x-731/3x=0

We multiply all the terms by the denominator


60x*3x-731=0

Wy multiply elements

180x^2-731=0

a = 180; b = 0; c = -731;
Δ = b2-4ac
Δ = 02-4·180·(-731)
Δ = 526320
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:

$\sqrt{\Delta}=\sqrt{526320}=\sqrt{144*3655}=\sqrt{144}*\sqrt{3655}=12\sqrt{3655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3655}}{2*180}=\frac{0-12\sqrt{3655}}{360}
=-\frac{12\sqrt{3655}}{360}
=-\frac{\sqrt{3655}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3655}}{2*180}=\frac{0+12\sqrt{3655}}{360}
=\frac{12\sqrt{3655}}{360}
=\frac{\sqrt{3655}}{30}
$