2(x+46)=3,174/x

Solution for 2(x+46)=3,174/x equation:

2(x+46)=3.174/x

We move all terms to the left:

2(x+46)-(3.174/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

2(x+46)-(+3.174/x)=0

We multiply parentheses

2x-(+3.174/x)+92=0

We get rid of parentheses

2x-3.174/x+92=0

We multiply all the terms by the denominator


2x*x+92*x-3.174=0

We add all the numbers together, and all the variables

92x+2x*x-3.174=0

Wy multiply elements

2x^2+92x-3.174=0

a = 2; b = 92; c = -3.174;
Δ = b2-4ac
Δ = 922-4·2·(-3.174)
Δ = 8489.392
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{-(92)-\sqrt{8489.392}}{2*2}=\frac{-92-\sqrt{8489.392}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+\sqrt{8489.392}}{2*2}=\frac{-92+\sqrt{8489.392}}{4}
$