9/x=3/2x+75

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Solution for 9/x=3/2x+75 equation:



9/x=3/2x+75
We move all terms to the left:
9/x-(3/2x+75)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 2x+75)!=0
x∈R
We get rid of parentheses
9/x-3/2x-75=0
We calculate fractions
18x/2x^2+(-3x)/2x^2-75=0
We multiply all the terms by the denominator
18x+(-3x)-75*2x^2=0
Wy multiply elements
-150x^2+18x+(-3x)=0
We get rid of parentheses
-150x^2+18x-3x=0
We add all the numbers together, and all the variables
-150x^2+15x=0
a = -150; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-150)·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*-150}=\frac{-30}{-300} =1/10 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-150}=\frac{0}{-300} =0 $

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