1/4x+210=x

Solution for 1/4x+210=x equation:

1/4x+210=x

We move all terms to the left:

1/4x+210-(x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/4x+210=0

We multiply all the terms by the denominator


-1x*4x+210*4x+1=0

Wy multiply elements

-4x^2+840x+1=0

a = -4; b = 840; c = +1;
Δ = b2-4ac
Δ = 8402-4·(-4)·1
Δ = 705616
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:

$\sqrt{\Delta}=\sqrt{705616}=\sqrt{16*44101}=\sqrt{16}*\sqrt{44101}=4\sqrt{44101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(840)-4\sqrt{44101}}{2*-4}=\frac{-840-4\sqrt{44101}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(840)+4\sqrt{44101}}{2*-4}=\frac{-840+4\sqrt{44101}}{-8}
$