10/x=5x/2x+30

Solution for 10/x=5x/2x+30 equation:

10/x=5x/2x+30

We move all terms to the left:

10/x-(5x/2x+30)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+30)!=0

x∈R


We get rid of parentheses

10/x-5x/2x-30=0

We calculate fractions


(-5x^2)/2x^2+20x/2x^2-30=0

We multiply all the terms by the denominator


(-5x^2)+20x-30*2x^2=0

Wy multiply elements

(-5x^2)-60x^2+20x=0

We get rid of parentheses

-5x^2-60x^2+20x=0

We add all the numbers together, and all the variables

-65x^2+20x=0

a = -65; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-65)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-65}=\frac{-40}{-130}
=4/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-65}=\frac{0}{-130}
=0
$