X(1/7)+x(5/6)=x

Solution for X(1/7)+x(5/6)=x equation:

X(1/7)+X(5/6)=X

We move all terms to the left:

X(1/7)+X(5/6)-(X)=0

We add all the numbers together, and all the variables

X(+1/7)+X(+5/6)-X=0

We add all the numbers together, and all the variables

-1X+X(+1/7)+X(+5/6)=0

We multiply parentheses

X^2+5X^2-1X=0

We add all the numbers together, and all the variables

6X^2-1X=0

a = 6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·6·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*6}=\frac{0}{12}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*6}=\frac{2}{12}
=1/6
$