4/x+1-27/8=-1/4x+4

Solution for 4/x+1-27/8=-1/4x+4 equation:

4/x+1-27/8=-1/4x+4

We move all terms to the left:

4/x+1-27/8-(-1/4x+4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x+4)!=0

x∈R


We get rid of parentheses

4/x+1/4x-4+1-27/8=0

We calculate fractions


(-432x^2)/256x^2+1024x/256x^2+64x/256x^2-4+1=0

We add all the numbers together, and all the variables

(-432x^2)/256x^2+1024x/256x^2+64x/256x^2-3=0

We multiply all the terms by the denominator


(-432x^2)+1024x+64x-3*256x^2=0

We add all the numbers together, and all the variables

(-432x^2)+1088x-3*256x^2=0

Wy multiply elements

(-432x^2)-768x^2+1088x=0

We get rid of parentheses

-432x^2-768x^2+1088x=0

We add all the numbers together, and all the variables

-1200x^2+1088x=0

a = -1200; b = 1088; c = 0;
Δ = b2-4ac
Δ = 10882-4·(-1200)·0
Δ = 1183744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1183744}=1088$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1088)-1088}{2*-1200}=\frac{-2176}{-2400}
=68/75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1088)+1088}{2*-1200}=\frac{0}{-2400}
=0
$