1/x-3=4x/3x

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

1/x-3=4x/3x

We move all terms to the left:

1/x-3-(4x/3x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-4x^2)/3x^2+3x/3x^2-3=0

We multiply all the terms by the denominator


(-4x^2)+3x-3*3x^2=0

Wy multiply elements

(-4x^2)-9x^2+3x=0

We get rid of parentheses

-4x^2-9x^2+3x=0

We add all the numbers together, and all the variables

-13x^2+3x=0

a = -13; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-13)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-13}=\frac{-6}{-26}
=3/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-13}=\frac{0}{-26}
=0
$