5.5x=4/9x

Solution for 5.5x=4/9x equation:

5.5x=4/9x

We move all terms to the left:

5.5x-(4/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5.5x-(+4/9x)=0

We get rid of parentheses

5.5x-4/9x=0

We multiply all the terms by the denominator


(5.5x)*9x-4=0

We add all the numbers together, and all the variables

(+5.5x)*9x-4=0

We multiply parentheses

45x^2-4=0

a = 45; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·45·(-4)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*45}=\frac{0-12\sqrt{5}}{90}
=-\frac{12\sqrt{5}}{90}
=-\frac{2\sqrt{5}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*45}=\frac{0+12\sqrt{5}}{90}
=\frac{12\sqrt{5}}{90}
=\frac{2\sqrt{5}}{15}
$