1/x+3=4x+1

Solution for 1/x+3=4x+1 equation:

1/x+3=4x+1

We move all terms to the left:

1/x+3-(4x+1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

1/x-4x-1+3=0

We multiply all the terms by the denominator


-4x*x-1*x+3*x+1=0

We add all the numbers together, and all the variables

2x-4x*x+1=0

Wy multiply elements

-4x^2+2x+1=0

a = -4; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-4)·1
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*-4}=\frac{-2-2\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*-4}=\frac{-2+2\sqrt{5}}{-8}
$