9/5x-1-1/3x=3

Solution for 9/5x-1-1/3x=3 equation:

9/5x-1-1/3x=3

We move all terms to the left:

9/5x-1-1/3x-(3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

9/5x-1/3x-4=0

We calculate fractions


27x/15x^2+(-5x)/15x^2-4=0

We multiply all the terms by the denominator


27x+(-5x)-4*15x^2=0

Wy multiply elements

-60x^2+27x+(-5x)=0

We get rid of parentheses

-60x^2+27x-5x=0

We add all the numbers together, and all the variables

-60x^2+22x=0

a = -60; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-60)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-60}=\frac{-44}{-120}
=11/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-60}=\frac{0}{-120}
=0
$