2x=42/x+1

Solution for 2x=42/x+1 equation:

2x=42/x+1

We move all terms to the left:

2x-(42/x+1)=0


Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

2x-42/x-1=0

We multiply all the terms by the denominator


2x*x-1*x-42=0

We add all the numbers together, and all the variables

-1x+2x*x-42=0

Wy multiply elements

2x^2-1x-42=0

a = 2; b = -1; c = -42;
Δ = b2-4ac
Δ = -12-4·2·(-42)
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{337}}{2*2}=\frac{1-\sqrt{337}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{337}}{2*2}=\frac{1+\sqrt{337}}{4}
$