1/5x+1/6x=13

Solution for 1/5x+1/6x=13 equation:

1/5x+1/6x=13

We move all terms to the left:

1/5x+1/6x-(13)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


6x/30x^2+5x/30x^2-13=0

We multiply all the terms by the denominator


6x+5x-13*30x^2=0

We add all the numbers together, and all the variables

11x-13*30x^2=0

Wy multiply elements

-390x^2+11x=0

a = -390; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-390)·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*-390}=\frac{-22}{-780}
=11/390
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-390}=\frac{0}{-780}
=0
$