210=x+1/4x

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

210=x+1/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-x-1/4x+210=0

We multiply all the terms by the denominator


-x*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 = 705584
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:

$\sqrt{\Delta}=\sqrt{705584}=\sqrt{16*44099}=\sqrt{16}*\sqrt{44099}=4\sqrt{44099}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(840)-4\sqrt{44099}}{2*-4}=\frac{-840-4\sqrt{44099}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(840)+4\sqrt{44099}}{2*-4}=\frac{-840+4\sqrt{44099}}{-8}
$