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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

4/x-4/4x+10=0

We calculate fractions


16x/4x^2+(-4x)/4x^2+10=0

We multiply all the terms by the denominator


16x+(-4x)+10*4x^2=0

Wy multiply elements

40x^2+16x+(-4x)=0

We get rid of parentheses

40x^2+16x-4x=0

We add all the numbers together, and all the variables

40x^2+12x=0

a = 40; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·40·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*40}=\frac{-24}{80}
=-3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*40}=\frac{0}{80}
=0
$