1/5x+2/3x=13

Solution for 1/5x+2/3x=13 equation:

1/5x+2/3x=13

We move all terms to the left:

1/5x+2/3x-(13)=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 calculate fractions


3x/15x^2+10x/15x^2-13=0

We multiply all the terms by the denominator


3x+10x-13*15x^2=0

We add all the numbers together, and all the variables

13x-13*15x^2=0

Wy multiply elements

-195x^2+13x=0

a = -195; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-195)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-195}=\frac{-26}{-390}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-195}=\frac{0}{-390}
=0
$