7x-6/6x=9

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 = b2-4ac
Δ = -542-4·42·(-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}
$