-1/4x-1=x+5

Solution for -1/4x-1=x+5 equation:

-1/4x-1=x+5

We move all terms to the left:

-1/4x-1-(x+5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-1/4x-x-5-1=0

We multiply all the terms by the denominator


-x*4x-5*4x-1*4x-1=0

Wy multiply elements

-4x^2-20x-4x-1=0

We add all the numbers together, and all the variables

-4x^2-24x-1=0

a = -4; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·(-4)·(-1)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{35}}{2*-4}=\frac{24-4\sqrt{35}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{35}}{2*-4}=\frac{24+4\sqrt{35}}{-8}
$