4/5x-4/1x=11

Solution for 4/5x-4/1x=11 equation:

4/5x-4/1x=11

We move all terms to the left:

4/5x-4/1x-(11)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 1x!=0

x∈R


We calculate fractions


4x/5x^2+(-20x)/5x^2-11=0

We multiply all the terms by the denominator


4x+(-20x)-11*5x^2=0

Wy multiply elements

-55x^2+4x+(-20x)=0

We get rid of parentheses

-55x^2+4x-20x=0

We add all the numbers together, and all the variables

-55x^2-16x=0

a = -55; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-55)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-55}=\frac{0}{-110}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-55}=\frac{32}{-110}
=-16/55
$