9/x=3/2x+30

Solution for 9/x=3/2x+30 equation:

9/x=3/2x+30

We move all terms to the left:

9/x-(3/2x+30)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

9/x-3/2x-30=0

We calculate fractions


18x/2x^2+(-3x)/2x^2-30=0

We multiply all the terms by the denominator


18x+(-3x)-30*2x^2=0

Wy multiply elements

-60x^2+18x+(-3x)=0

We get rid of parentheses

-60x^2+18x-3x=0

We add all the numbers together, and all the variables

-60x^2+15x=0

a = -60; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-60)·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*-60}=\frac{-30}{-120}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-60}=\frac{0}{-120}
=0
$