1/6x+1/7x=13

Solution for 1/6x+1/7x=13 equation:

1/6x+1/7x=13

We move all terms to the left:

1/6x+1/7x-(13)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We calculate fractions


7x/42x^2+6x/42x^2-13=0

We multiply all the terms by the denominator


7x+6x-13*42x^2=0

We add all the numbers together, and all the variables

13x-13*42x^2=0

Wy multiply elements

-546x^2+13x=0

a = -546; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-546)·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*-546}=\frac{-26}{-1092}
=1/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-546}=\frac{0}{-1092}
=0
$