x(x+2)=16/9

Solution for x(x+2)=16/9 equation:

x(x+2)=16/9

We move all terms to the left:

x(x+2)-(16/9)=0

We add all the numbers together, and all the variables

x(x+2)-(+16/9)=0

We multiply parentheses

x^2+2x-(+16/9)=0

We get rid of parentheses

x^2+2x-16/9=0

We multiply all the terms by the denominator


x^2*9+2x*9-16=0

Wy multiply elements

9x^2+18x-16=0

a = 9; b = 18; c = -16;
Δ = b2-4ac
Δ = 182-4·9·(-16)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*9}=\frac{-48}{18}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*9}=\frac{12}{18}
=2/3
$