1/4x+11=4x

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

1/4x+11=4x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-16x^2+44x+1=0

a = -16; b = 44; c = +1;
Δ = b2-4ac
Δ = 442-4·(-16)·1
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-20\sqrt{5}}{2*-16}=\frac{-44-20\sqrt{5}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+20\sqrt{5}}{2*-16}=\frac{-44+20\sqrt{5}}{-32}
$