3x-5=4/x=2

Solution for 3x-5=4/x=2 equation:

3x-5=4/x=2

We move all terms to the left:

3x-5-(4/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-(+4/x)-5=0

We get rid of parentheses

3x-4/x-5=0

We multiply all the terms by the denominator


3x*x-5*x-4=0

We add all the numbers together, and all the variables

-5x+3x*x-4=0

Wy multiply elements

3x^2-5x-4=0

a = 3; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·3·(-4)
Δ = 73
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{-(-5)-\sqrt{73}}{2*3}=\frac{5-\sqrt{73}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*3}=\frac{5+\sqrt{73}}{6}
$