9/x+3/2x=3

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

9/x+3/2x=3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

21x-3*2x^2=0

Wy multiply elements

-6x^2+21x=0

a = -6; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-6)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-6}=\frac{-42}{-12}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-6}=\frac{0}{-12}
=0
$