5x/x^2+1=15

Solution for 5x/x^2+1=15 equation:

5x/x^2+1=15

We move all terms to the left:

5x/x^2+1-(15)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

5x/x^2-14=0

We multiply all the terms by the denominator


5x-14*x^2=0

We add all the numbers together, and all the variables

-14x^2+5x=0

a = -14; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-14)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-14}=\frac{-10}{-28}
=5/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-14}=\frac{0}{-28}
=0
$