x*x+8/9=2x

Solution for x*x+8/9=2x equation:

x*x+8/9=2x

We move all terms to the left:

x*x+8/9-(2x)=0

We add all the numbers together, and all the variables

-2x+x*x+8/9=0

Wy multiply elements

x^2-2x+8/9=0

We multiply all the terms by the denominator


x^2*9-2x*9+8=0

Wy multiply elements

9x^2-18x+8=0

a = 9; b = -18; c = +8;
Δ = b2-4ac
Δ = -182-4·9·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*9}=\frac{12}{18}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*9}=\frac{24}{18}
=1+1/3
$