2x-5=42/x

Solution for 2x-5=42/x equation:

2x-5=42/x

We move all terms to the left:

2x-5-(42/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

2x-(+42/x)-5=0

We get rid of parentheses

2x-42/x-5=0

We multiply all the terms by the denominator


2x*x-5*x-42=0

We add all the numbers together, and all the variables

-5x+2x*x-42=0

Wy multiply elements

2x^2-5x-42=0

a = 2; b = -5; c = -42;
Δ = b2-4ac
Δ = -52-4·2·(-42)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*2}=\frac{-14}{4}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*2}=\frac{24}{4}
=6
$