-2/9x-8/45+1/5x=-63

Solution for -2/9x-8/45+1/5x=-63 equation:

-2/9x-8/45+1/5x=-63

We move all terms to the left:

-2/9x-8/45+1/5x-(-63)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-2/9x+1/5x+63-8/45=0

We calculate fractions


(-1800x^2)/8100x^2+(-1800x)/8100x^2+1620x/8100x^2+63=0

We multiply all the terms by the denominator


(-1800x^2)+(-1800x)+1620x+63*8100x^2=0

We add all the numbers together, and all the variables

(-1800x^2)+1620x+(-1800x)+63*8100x^2=0

Wy multiply elements

(-1800x^2)+510300x^2+1620x+(-1800x)=0

We get rid of parentheses

-1800x^2+510300x^2+1620x-1800x=0

We add all the numbers together, and all the variables

508500x^2-180x=0

a = 508500; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·508500·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*508500}=\frac{0}{1017000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*508500}=\frac{360}{1017000}
=1/2825
$