(4x^2+30x+31)/(x+6)=0

Solution for (4x^2+30x+31)/(x+6)=0 equation:

(4x^2+30x+31)/(x+6)=0


Domain of the equation: (x+6)!=0

We move all terms containing x to the left, all other terms to the right

x!=-6

x∈R


We multiply all the terms by the denominator


(4x^2+30x+31)=0

We get rid of parentheses

4x^2+30x+31=0

a = 4; b = 30; c = +31;
Δ = b2-4ac
Δ = 302-4·4·31
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{101}}{2*4}=\frac{-30-2\sqrt{101}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{101}}{2*4}=\frac{-30+2\sqrt{101}}{8}
$