100+1/4x=x

Solution for 100+1/4x=x equation:

100+1/4x=x

We move all terms to the left:

100+1/4x-(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+100=0

We multiply all the terms by the denominator


-1x*4x+100*4x+1=0

Wy multiply elements

-4x^2+400x+1=0

a = -4; b = 400; c = +1;
Δ = b2-4ac
Δ = 4002-4·(-4)·1
Δ = 160016
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:

$\sqrt{\Delta}=\sqrt{160016}=\sqrt{16*10001}=\sqrt{16}*\sqrt{10001}=4\sqrt{10001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-4\sqrt{10001}}{2*-4}=\frac{-400-4\sqrt{10001}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+4\sqrt{10001}}{2*-4}=\frac{-400+4\sqrt{10001}}{-8}
$