17x-36+(2/x)=90

Solution for 17x-36+(2/x)=90 equation:

17x-36+(2/x)=90

We move all terms to the left:

17x-36+(2/x)-(90)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

17x+(+2/x)-36-90=0

We add all the numbers together, and all the variables

17x+(+2/x)-126=0

We get rid of parentheses

17x+2/x-126=0

We multiply all the terms by the denominator


17x*x-126*x+2=0

We add all the numbers together, and all the variables

-126x+17x*x+2=0

Wy multiply elements

17x^2-126x+2=0

a = 17; b = -126; c = +2;
Δ = b2-4ac
Δ = -1262-4·17·2
Δ = 15740
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:

$\sqrt{\Delta}=\sqrt{15740}=\sqrt{4*3935}=\sqrt{4}*\sqrt{3935}=2\sqrt{3935}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3935}}{2*17}=\frac{126-2\sqrt{3935}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3935}}{2*17}=\frac{126+2\sqrt{3935}}{34}
$