1/4x+16=x-4

Solution for 1/4x+16=x-4 equation:

1/4x+16=x-4

We move all terms to the left:

1/4x+16-(x-4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x+4+16=0

We multiply all the terms by the denominator


-x*4x+4*4x+16*4x+1=0

Wy multiply elements

-4x^2+16x+64x+1=0

We add all the numbers together, and all the variables

-4x^2+80x+1=0

a = -4; b = 80; c = +1;
Δ = b2-4ac
Δ = 802-4·(-4)·1
Δ = 6416
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:

$\sqrt{\Delta}=\sqrt{6416}=\sqrt{16*401}=\sqrt{16}*\sqrt{401}=4\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-4\sqrt{401}}{2*-4}=\frac{-80-4\sqrt{401}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+4\sqrt{401}}{2*-4}=\frac{-80+4\sqrt{401}}{-8}
$