(X/6)-(x/7)=(5/6)

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

(X/6)-(X/7)=(5/6)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-216X^2)/()+7X/()+()/()=0

We add all the numbers together, and all the variables

(-216X^2)/()+7X/()+1=0

We multiply all the terms by the denominator


(-216X^2)+7X+1*()=0

We add all the numbers together, and all the variables

(-216X^2)+7X=0

We get rid of parentheses

-216X^2+7X=0

a = -216; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-216)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-216}=\frac{-14}{-432}
=7/216
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-216}=\frac{0}{-432}
=0
$