1/3x+2/5x-3=2

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

1/3x+2/5x-3=2

We move all terms to the left:

1/3x+2/5x-3-(2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x+2/5x-5=0

We calculate fractions


5x/15x^2+6x/15x^2-5=0

We multiply all the terms by the denominator


5x+6x-5*15x^2=0

We add all the numbers together, and all the variables

11x-5*15x^2=0

Wy multiply elements

-75x^2+11x=0

a = -75; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-75)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-75}=\frac{-22}{-150}
=11/75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-75}=\frac{0}{-150}
=0
$