(4/9)x=8/45

Solution for (4/9)x=8/45 equation:

(4/9)x=8/45

We move all terms to the left:

(4/9)x-(8/45)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4/9)x-(+8/45)=0

We multiply parentheses

4x^2-(+8/45)=0

We get rid of parentheses

4x^2-8/45=0

We multiply all the terms by the denominator


4x^2*45-8=0

Wy multiply elements

180x^2-8=0

a = 180; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·180·(-8)
Δ = 5760
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{10}}{2*180}=\frac{0-24\sqrt{10}}{360}
=-\frac{24\sqrt{10}}{360}
=-\frac{\sqrt{10}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{10}}{2*180}=\frac{0+24\sqrt{10}}{360}
=\frac{24\sqrt{10}}{360}
=\frac{\sqrt{10}}{15}
$