(x^2+7x+1)/x+4=0

Solution for (x^2+7x+1)/x+4=0 equation:

(x^2+7x+1)/x+4=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


(x^2+7x+1)+4*x=0

We add all the numbers together, and all the variables

4x+(x^2+7x+1)=0

We get rid of parentheses

x^2+4x+7x+1=0

We add all the numbers together, and all the variables

x^2+11x+1=0

a = 1; b = 11; c = +1;
Δ = b2-4ac
Δ = 112-4·1·1
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{13}}{2*1}=\frac{-11-3\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{13}}{2*1}=\frac{-11+3\sqrt{13}}{2}
$