(9x^2+66x+21)/(x+7)=0

Solution for (9x^2+66x+21)/(x+7)=0 equation:

(9x^2+66x+21)/(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


(9x^2+66x+21)=0

We get rid of parentheses

9x^2+66x+21=0

a = 9; b = 66; c = +21;
Δ = b2-4ac
Δ = 662-4·9·21
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-60}{2*9}=\frac{-126}{18}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+60}{2*9}=\frac{-6}{18}
=-1/3
$