((4*(x*x))+34x+43)/(x+7)=0

Solution for ((4*(x*x))+34x+43)/(x+7)=0 equation:

((4(x*x))+34x+43)/(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 add all the numbers together, and all the variables

((4(+x*x))+34x+43)/(x+7)=0

We multiply all the terms by the denominator


((4(+x*x))+34x+43)=0


We calculate terms in parentheses: +((4(+x*x))+34x+43), so:

(4(+x*x))+34x+43

We add all the numbers together, and all the variables

34x+(4(+x*x))+43


We calculate terms in parentheses: +(4(+x*x)), so:

4(+x*x)

We multiply parentheses

4x^2

Back to the equation:

+(4x^2)


determiningTheFunctionDomain
4x^2+34x+43

Back to the equation:

+(4x^2+34x+43)


We get rid of parentheses

4x^2+34x+43=0

a = 4; b = 34; c = +43;
Δ = b2-4ac
Δ = 342-4·4·43
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-6\sqrt{13}}{2*4}=\frac{-34-6\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+6\sqrt{13}}{2*4}=\frac{-34+6\sqrt{13}}{8}
$