6x+7-2/x=9

Solution for 6x+7-2/x=9 equation:

6x+7-2/x=9

We move all terms to the left:

6x+7-2/x-(9)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

6x-2/x-2=0

We multiply all the terms by the denominator


6x*x-2*x-2=0

We add all the numbers together, and all the variables

-2x+6x*x-2=0

Wy multiply elements

6x^2-2x-2=0

a = 6; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·6·(-2)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*6}=\frac{2-2\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*6}=\frac{2+2\sqrt{13}}{12}
$