9/x+12=14x

Solution for 9/x+12=14x equation:

9/x+12=14x

We move all terms to the left:

9/x+12-(14x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-14x+9/x+12=0

We multiply all the terms by the denominator


-14x*x+12*x+9=0

We add all the numbers together, and all the variables

12x-14x*x+9=0

Wy multiply elements

-14x^2+12x+9=0

a = -14; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·(-14)·9
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18\sqrt{2}}{2*-14}=\frac{-12-18\sqrt{2}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18\sqrt{2}}{2*-14}=\frac{-12+18\sqrt{2}}{-28}
$