4x-5=3/x

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

4x-5=3/x

We move all terms to the left:

4x-5-(3/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

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

We get rid of parentheses

4x-3/x-5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2-5x-3=0

a = 4; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·4·(-3)
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*4}=\frac{5-\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*4}=\frac{5+\sqrt{73}}{8}
$