3/x+1=5x

Solution for 3/x+1=5x equation:

3/x+1=5x

We move all terms to the left:

3/x+1-(5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+3/x+1=0

We multiply all the terms by the denominator


-5x*x+1*x+3=0

We add all the numbers together, and all the variables

x-5x*x+3=0

Wy multiply elements

-5x^2+x+3=0

a = -5; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-5)·3
Δ = 61
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{-(1)-\sqrt{61}}{2*-5}=\frac{-1-\sqrt{61}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{61}}{2*-5}=\frac{-1+\sqrt{61}}{-10}
$