4200/46x=x

Solution for 4200/46x=x equation:

4200/46x=x

We move all terms to the left:

4200/46x-(x)=0


Domain of the equation: 46x!=0

x!=0/46

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4200/46x=0

We multiply all the terms by the denominator


-1x*46x+4200=0

Wy multiply elements

-46x^2+4200=0

a = -46; b = 0; c = +4200;
Δ = b2-4ac
Δ = 02-4·(-46)·4200
Δ = 772800
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:

$\sqrt{\Delta}=\sqrt{772800}=\sqrt{1600*483}=\sqrt{1600}*\sqrt{483}=40\sqrt{483}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{483}}{2*-46}=\frac{0-40\sqrt{483}}{-92}
=-\frac{40\sqrt{483}}{-92}
=-\frac{10\sqrt{483}}{-23}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{483}}{2*-46}=\frac{0+40\sqrt{483}}{-92}
=\frac{40\sqrt{483}}{-92}
=\frac{10\sqrt{483}}{-23}
$