9/x-4+2=17x

Solution for 9/x-4+2=17x equation:

9/x-4+2=17x

We move all terms to the left:

9/x-4+2-(17x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-17x+9/x-2=0

We multiply all the terms by the denominator


-17x*x-2*x+9=0

We add all the numbers together, and all the variables

-2x-17x*x+9=0

Wy multiply elements

-17x^2-2x+9=0

a = -17; b = -2; c = +9;
Δ = b2-4ac
Δ = -22-4·(-17)·9
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{154}}{2*-17}=\frac{2-2\sqrt{154}}{-34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{154}}{2*-17}=\frac{2+2\sqrt{154}}{-34}
$