8/x=5/2x+11

Solution for 8/x=5/2x+11 equation:

8/x=5/2x+11

We move all terms to the left:

8/x-(5/2x+11)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+11)!=0

x∈R


We get rid of parentheses

8/x-5/2x-11=0

We calculate fractions


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

We multiply all the terms by the denominator


16x+(-5x)-11*2x^2=0

Wy multiply elements

-22x^2+16x+(-5x)=0

We get rid of parentheses

-22x^2+16x-5x=0

We add all the numbers together, and all the variables

-22x^2+11x=0

a = -22; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-22)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-22}=\frac{-22}{-44}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-22}=\frac{0}{-44}
=0
$