6x-53=9/x

Solution for 6x-53=9/x equation:

6x-53=9/x

We move all terms to the left:

6x-53-(9/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+9/x)-53=0

We get rid of parentheses

6x-9/x-53=0

We multiply all the terms by the denominator


6x*x-53*x-9=0

We add all the numbers together, and all the variables

-53x+6x*x-9=0

Wy multiply elements

6x^2-53x-9=0

a = 6; b = -53; c = -9;
Δ = b2-4ac
Δ = -532-4·6·(-9)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-55}{2*6}=\frac{-2}{12}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+55}{2*6}=\frac{108}{12}
=9
$