8/x=5/2x+33

Solution for 8/x=5/2x+33 equation:

8/x=5/2x+33

We move all terms to the left:

8/x-(5/2x+33)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+33)!=0

x∈R


We get rid of parentheses

8/x-5/2x-33=0

We calculate fractions


16x/2x^2+(-5x)/2x^2-33=0

We multiply all the terms by the denominator


16x+(-5x)-33*2x^2=0

Wy multiply elements

-66x^2+16x+(-5x)=0

We get rid of parentheses

-66x^2+16x-5x=0

We add all the numbers together, and all the variables

-66x^2+11x=0

a = -66; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-66)·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*-66}=\frac{-22}{-132}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-66}=\frac{0}{-132}
=0
$