(4x2+28x+27)/x+6=0

Solution for (4x2+28x+27)/x+6=0 equation:

(4x^2+28x+27)/x+6=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


(4x^2+28x+27)+6*x=0

We add all the numbers together, and all the variables

6x+(4x^2+28x+27)=0

We get rid of parentheses

4x^2+6x+28x+27=0

We add all the numbers together, and all the variables

4x^2+34x+27=0

a = 4; b = 34; c = +27;
Δ = b2-4ac
Δ = 342-4·4·27
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{181}}{2*4}=\frac{-34-2\sqrt{181}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{181}}{2*4}=\frac{-34+2\sqrt{181}}{8}
$