(4x^2+34x+44)/(x+7)=0

Solution for (4x^2+34x+44)/(x+7)=0 equation:

(4x^2+34x+44)/(x+7)=0


Domain of the equation: (x+7)!=0

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

x!=-7

x∈R


We multiply all the terms by the denominator


(4x^2+34x+44)=0

We get rid of parentheses

4x^2+34x+44=0

a = 4; b = 34; c = +44;
Δ = b2-4ac
Δ = 342-4·4·44
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{113}}{2*4}=\frac{-34-2\sqrt{113}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{113}}{2*4}=\frac{-34+2\sqrt{113}}{8}
$