3/x+5/2x=-6

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Solution for 3/x+5/2x=-6 equation:



3/x+5/2x=-6
We move all terms to the left:
3/x+5/2x-(-6)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
3/x+5/2x+6=0
We calculate fractions
6x/2x^2+5x/2x^2+6=0
We multiply all the terms by the denominator
6x+5x+6*2x^2=0
We add all the numbers together, and all the variables
11x+6*2x^2=0
Wy multiply elements
12x^2+11x=0
a = 12; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·12·0
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*12}=\frac{-22}{24} =-11/12 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*12}=\frac{0}{24} =0 $

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