-1/4x+2+5=-x

Solution for -1/4x+2+5=-x equation:

-1/4x+2+5=-x

We move all terms to the left:

-1/4x+2+5-(-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

-1/4x-(-1x)+2+5=0

We add all the numbers together, and all the variables

-1/4x-(-1x)+7=0

We get rid of parentheses

-1/4x+1x+7=0

We multiply all the terms by the denominator


1x*4x+7*4x-1=0

Wy multiply elements

4x^2+28x-1=0

a = 4; b = 28; c = -1;
Δ = b2-4ac
Δ = 282-4·4·(-1)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-20\sqrt{2}}{2*4}=\frac{-28-20\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+20\sqrt{2}}{2*4}=\frac{-28+20\sqrt{2}}{8}
$