7/x=3,x

Solution for 7/x=3,x equation:

7/x=3.x

We move all terms to the left:

7/x-(3.x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7/x-(+3.x)=0

We get rid of parentheses

7/x-3.x=0

We multiply all the terms by the denominator


-(3.x)*x+7=0

We add all the numbers together, and all the variables

-(+3.x)*x+7=0

We multiply parentheses

-3x^2+7=0

a = -3; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-3)·7
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*-3}=\frac{0-2\sqrt{21}}{-6}
=-\frac{2\sqrt{21}}{-6}
=-\frac{\sqrt{21}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*-3}=\frac{0+2\sqrt{21}}{-6}
=\frac{2\sqrt{21}}{-6}
=\frac{\sqrt{21}}{-3}
$