3250/3x=x

Solution for 3250/3x=x equation:

3250/3x=x

We move all terms to the left:

3250/3x-(x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3250/3x=0

We multiply all the terms by the denominator


-1x*3x+3250=0

Wy multiply elements

-3x^2+3250=0

a = -3; b = 0; c = +3250;
Δ = b2-4ac
Δ = 02-4·(-3)·3250
Δ = 39000
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:

$\sqrt{\Delta}=\sqrt{39000}=\sqrt{100*390}=\sqrt{100}*\sqrt{390}=10\sqrt{390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{390}}{2*-3}=\frac{0-10\sqrt{390}}{-6}
=-\frac{10\sqrt{390}}{-6}
=-\frac{5\sqrt{390}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{390}}{2*-3}=\frac{0+10\sqrt{390}}{-6}
=\frac{10\sqrt{390}}{-6}
=\frac{5\sqrt{390}}{-3}
$