# 7x-6/6x=9

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## Solution for 7x-6/6x=9 equation:

7x-6/6x=9
We move all terms to the left:
7x-6/6x-(9)=0

Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R

We multiply all the terms by the denominator

7x*6x-9*6x-6=0
Wy multiply elements
42x^2-54x-6=0
a = 42; b = -54; c = -6;Δ = b2-4acΔ = -542-4·42·(-6)Δ = 3924The delta value is higher than zero, so the equation has two solutionsWe 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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