3+4x=45/x

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Solution for 3+4x=45/x equation:



3+4x=45/x
We move all terms to the left:
3+4x-(45/x)=0
Domain of the equation: x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
4x-(+45/x)+3=0
We get rid of parentheses
4x-45/x+3=0
We multiply all the terms by the denominator
4x*x+3*x-45=0
We add all the numbers together, and all the variables
3x+4x*x-45=0
Wy multiply elements
4x^2+3x-45=0
a = 4; b = 3; c = -45;
Δ = b2-4ac
Δ = 32-4·4·(-45)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*4}=\frac{-30}{8} =-3+3/4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*4}=\frac{24}{8} =3 $

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