x(x+3)=22/9

Solution for x(x+3)=22/9 equation:

x(x+3)=22/9

We move all terms to the left:

x(x+3)-(22/9)=0

We add all the numbers together, and all the variables

x(x+3)-(+22/9)=0

We multiply parentheses

x^2+3x-(+22/9)=0

We get rid of parentheses

x^2+3x-22/9=0

We multiply all the terms by the denominator


x^2*9+3x*9-22=0

Wy multiply elements

9x^2+27x-22=0

a = 9; b = 27; c = -22;
Δ = b2-4ac
Δ = 272-4·9·(-22)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-39}{2*9}=\frac{-66}{18}
=-3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+39}{2*9}=\frac{12}{18}
=2/3
$