1/4x+11=x

Solution for 1/4x+11=x equation:

1/4x+11=x

We move all terms to the left:

1/4x+11-(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+11=0

We multiply all the terms by the denominator


-1x*4x+11*4x+1=0

Wy multiply elements

-4x^2+44x+1=0

a = -4; b = 44; c = +1;
Δ = b2-4ac
Δ = 442-4·(-4)·1
Δ = 1952
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:

$\sqrt{\Delta}=\sqrt{1952}=\sqrt{16*122}=\sqrt{16}*\sqrt{122}=4\sqrt{122}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{122}}{2*-4}=\frac{-44-4\sqrt{122}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{122}}{2*-4}=\frac{-44+4\sqrt{122}}{-8}
$