2x+(102/x)=40

Solution for 2x+(102/x)=40 equation:

2x+(102/x)=40

We move all terms to the left:

2x+(102/x)-(40)=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+(+102/x)-40=0

We get rid of parentheses

2x+102/x-40=0

We multiply all the terms by the denominator


2x*x-40*x+102=0

We add all the numbers together, and all the variables

-40x+2x*x+102=0

Wy multiply elements

2x^2-40x+102=0

a = 2; b = -40; c = +102;
Δ = b2-4ac
Δ = -402-4·2·102
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-28}{2*2}=\frac{12}{4}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+28}{2*2}=\frac{68}{4}
=17
$