7/x=9x+6

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

7/x=9x+6

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

7/x-9x-6=0

We multiply all the terms by the denominator


-9x*x-6*x+7=0

We add all the numbers together, and all the variables

-6x-9x*x+7=0

Wy multiply elements

-9x^2-6x+7=0

a = -9; b = -6; c = +7;
Δ = b2-4ac
Δ = -62-4·(-9)·7
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{2}}{2*-9}=\frac{6-12\sqrt{2}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{2}}{2*-9}=\frac{6+12\sqrt{2}}{-18}
$