20/9x*2-23/3x+5=0

Solution for 20/9x*2-23/3x+5=0 equation:

20/9x*2-23/3x+5=0


Domain of the equation: 9x*2!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


60x/162x^2+(-828x)/162x^2+5=0

We multiply all the terms by the denominator


60x+(-828x)+5*162x^2=0

Wy multiply elements

810x^2+60x+(-828x)=0

We get rid of parentheses

810x^2+60x-828x=0

We add all the numbers together, and all the variables

810x^2-768x=0

a = 810; b = -768; c = 0;
Δ = b2-4ac
Δ = -7682-4·810·0
Δ = 589824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{589824}=768$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-768)-768}{2*810}=\frac{0}{1620}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-768)+768}{2*810}=\frac{1536}{1620}
=128/135
$