5x-2/3x+4=1

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Solution for 5x-2/3x+4=1 equation:



5x-2/3x+4=1
We move all terms to the left:
5x-2/3x+4-(1)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
5x-2/3x+3=0
We multiply all the terms by the denominator
5x*3x+3*3x-2=0
Wy multiply elements
15x^2+9x-2=0
a = 15; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·15·(-2)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{201}}{2*15}=\frac{-9-\sqrt{201}}{30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{201}}{2*15}=\frac{-9+\sqrt{201}}{30} $

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