2X+3=10/x

Solution for 2X+3=10/x equation:

2X+3=10/X

We move all terms to the left:

2X+3-(10/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-(+10/X)+3=0

We get rid of parentheses

2X-10/X+3=0

We multiply all the terms by the denominator


2X*X+3*X-10=0

We add all the numbers together, and all the variables

3X+2X*X-10=0

Wy multiply elements

2X^2+3X-10=0

a = 2; b = 3; c = -10;
Δ = b2-4ac
Δ = 32-4·2·(-10)
Δ = 89
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{-(3)-\sqrt{89}}{2*2}=\frac{-3-\sqrt{89}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{89}}{2*2}=\frac{-3+\sqrt{89}}{4}
$