3x+4=23/x

Solution for 3x+4=23/x equation:

3x+4=23/x

We move all terms to the left:

3x+4-(23/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

3x-(+23/x)+4=0

We get rid of parentheses

3x-23/x+4=0

We multiply all the terms by the denominator


3x*x+4*x-23=0

We add all the numbers together, and all the variables

4x+3x*x-23=0

Wy multiply elements

3x^2+4x-23=0

a = 3; b = 4; c = -23;
Δ = b2-4ac
Δ = 42-4·3·(-23)
Δ = 292
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{73}}{2*3}=\frac{-4-2\sqrt{73}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{73}}{2*3}=\frac{-4+2\sqrt{73}}{6}
$