7/x-4=9x

Solution for 7/x-4=9x equation:

7/x-4=9x

We move all terms to the left:

7/x-4-(9x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-9x+7/x-4=0

We multiply all the terms by the denominator


-9x*x-4*x+7=0

We add all the numbers together, and all the variables

-4x-9x*x+7=0

Wy multiply elements

-9x^2-4x+7=0

a = -9; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-9)·7
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{67}}{2*-9}=\frac{4-2\sqrt{67}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{67}}{2*-9}=\frac{4+2\sqrt{67}}{-18}
$