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7x-6/6x=9

We move all terms to the left:

7x-6/6x-(9)=0

Domain of the equation: 6x!=0We multiply all the terms by the denominator

x!=0/6

x!=0

x∈R

7x*6x-9*6x-6=0

Wy multiply elements

42x^2-54x-6=0

a = 42; b = -54; c = -6;

Δ = b^{2}-4ac

Δ = -54^{2}-4·42·(-6)

Δ = 3924

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}$

The end solution:

$\sqrt{\Delta}=\sqrt{3924}=\sqrt{36*109}=\sqrt{36}*\sqrt{109}=6\sqrt{109}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{109}}{2*42}=\frac{54-6\sqrt{109}}{84} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{109}}{2*42}=\frac{54+6\sqrt{109}}{84} $

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