(42/x)+2x=20

Solution for (42/x)+2x=20 equation:

(42/x)+2x=20

We move all terms to the left:

(42/x)+2x-(20)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+42/x)+2x-20=0

We add all the numbers together, and all the variables

2x+(+42/x)-20=0

We get rid of parentheses

2x+42/x-20=0

We multiply all the terms by the denominator


2x*x-20*x+42=0

We add all the numbers together, and all the variables

-20x+2x*x+42=0

Wy multiply elements

2x^2-20x+42=0

a = 2; b = -20; c = +42;
Δ = b2-4ac
Δ = -202-4·2·42
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8}{2*2}=\frac{12}{4}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8}{2*2}=\frac{28}{4}
=7
$