53-(2x+17)=53/x

Solution for 53-(2x+17)=53/x equation:

53-(2x+17)=53/x

We move all terms to the left:

53-(2x+17)-(53/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

-(2x+17)-(+53/x)+53=0

We get rid of parentheses

-2x-53/x-17+53=0

We multiply all the terms by the denominator


-2x*x-17*x+53*x-53=0

We add all the numbers together, and all the variables

36x-2x*x-53=0

Wy multiply elements

-2x^2+36x-53=0

a = -2; b = 36; c = -53;
Δ = b2-4ac
Δ = 362-4·(-2)·(-53)
Δ = 872
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:

$\sqrt{\Delta}=\sqrt{872}=\sqrt{4*218}=\sqrt{4}*\sqrt{218}=2\sqrt{218}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{218}}{2*-2}=\frac{-36-2\sqrt{218}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{218}}{2*-2}=\frac{-36+2\sqrt{218}}{-4}
$