1/x+4/3x-1=0

Solution for 1/x+4/3x-1=0 equation:

1/x+4/3x-1=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


3x/3x^2+4x/3x^2-1=0

We multiply all the terms by the denominator


3x+4x-1*3x^2=0

We add all the numbers together, and all the variables

7x-1*3x^2=0

Wy multiply elements

-3x^2+7x=0

a = -3; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-3)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-3}=\frac{-14}{-6}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-3}=\frac{0}{-6}
=0
$