4/x+3=16/5x+11

Solution for 4/x+3=16/5x+11 equation:

4/x+3=16/5x+11

We move all terms to the left:

4/x+3-(16/5x+11)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+11)!=0

x∈R


We get rid of parentheses

4/x-16/5x-11+3=0

We calculate fractions


20x/5x^2+(-16x)/5x^2-11+3=0

We add all the numbers together, and all the variables

20x/5x^2+(-16x)/5x^2-8=0

We multiply all the terms by the denominator


20x+(-16x)-8*5x^2=0

Wy multiply elements

-40x^2+20x+(-16x)=0

We get rid of parentheses

-40x^2+20x-16x=0

We add all the numbers together, and all the variables

-40x^2+4x=0

a = -40; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-40)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-40}=\frac{-8}{-80}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-40}=\frac{0}{-80}
=0
$