10/x=5/2x+33

Solution for 10/x=5/2x+33 equation:

10/x=5/2x+33

We move all terms to the left:

10/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

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

We calculate fractions


20x/2x^2+(-5x)/2x^2-33=0

We multiply all the terms by the denominator


20x+(-5x)-33*2x^2=0

Wy multiply elements

-66x^2+20x+(-5x)=0

We get rid of parentheses

-66x^2+20x-5x=0

We add all the numbers together, and all the variables

-66x^2+15x=0

a = -66; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-66)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-66}=\frac{-30}{-132}
=5/22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-66}=\frac{0}{-132}
=0
$