2x-x^2=5/9

Solution for 2x-x^2=5/9 equation:

2x-x^2=5/9

We move all terms to the left:

2x-x^2-(5/9)=0

We add all the numbers together, and all the variables

-x^2+2x-(+5/9)=0

We add all the numbers together, and all the variables

-1x^2+2x-(+5/9)=0

We get rid of parentheses

-1x^2+2x-5/9=0

We multiply all the terms by the denominator


-1x^2*9+2x*9-5=0

Wy multiply elements

-9x^2+18x-5=0

a = -9; b = 18; c = -5;
Δ = b2-4ac
Δ = 182-4·(-9)·(-5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12}{2*-9}=\frac{-30}{-18}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12}{2*-9}=\frac{-6}{-18}
=1/3
$