x^2+6x+9=49/9

Solution for x^2+6x+9=49/9 equation:

x^2+6x+9=49/9

We move all terms to the left:

x^2+6x+9-(49/9)=0

We add all the numbers together, and all the variables

x^2+6x+9-(+49/9)=0

We get rid of parentheses

x^2+6x+9-49/9=0

We multiply all the terms by the denominator


x^2*9+6x*9-49+9*9=0

We add all the numbers together, and all the variables

x^2*9+6x*9+32=0

Wy multiply elements

9x^2+54x+32=0

a = 9; b = 54; c = +32;
Δ = b2-4ac
Δ = 542-4·9·32
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-42}{2*9}=\frac{-96}{18}
=-5+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+42}{2*9}=\frac{-12}{18}
=-2/3
$