1/4x+4=-x-4

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

1/4x+4=-x-4

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/4x+1x+4+4=0

We multiply all the terms by the denominator


1x*4x+4*4x+4*4x+1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2+32x+1=0

a = 4; b = 32; c = +1;
Δ = b2-4ac
Δ = 322-4·4·1
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-12\sqrt{7}}{2*4}=\frac{-32-12\sqrt{7}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+12\sqrt{7}}{2*4}=\frac{-32+12\sqrt{7}}{8}
$