57-9/x=3x

Solution for 57-9/x=3x equation:

57-9/x=3x

We move all terms to the left:

57-9/x-(3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-3x-9/x+57=0

We multiply all the terms by the denominator


-3x*x+57*x-9=0

We add all the numbers together, and all the variables

57x-3x*x-9=0

Wy multiply elements

-3x^2+57x-9=0

a = -3; b = 57; c = -9;
Δ = b2-4ac
Δ = 572-4·(-3)·(-9)
Δ = 3141
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:

$\sqrt{\Delta}=\sqrt{3141}=\sqrt{9*349}=\sqrt{9}*\sqrt{349}=3\sqrt{349}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-3\sqrt{349}}{2*-3}=\frac{-57-3\sqrt{349}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+3\sqrt{349}}{2*-3}=\frac{-57+3\sqrt{349}}{-6}
$