4x-17=15/x

Solution for 4x-17=15/x equation:

4x-17=15/x

We move all terms to the left:

4x-17-(15/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-(+15/x)-17=0

We get rid of parentheses

4x-15/x-17=0

We multiply all the terms by the denominator


4x*x-17*x-15=0

We add all the numbers together, and all the variables

-17x+4x*x-15=0

Wy multiply elements

4x^2-17x-15=0

a = 4; b = -17; c = -15;
Δ = b2-4ac
Δ = -172-4·4·(-15)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-23}{2*4}=\frac{-6}{8}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+23}{2*4}=\frac{40}{8}
=5
$