(18-9)/3=9/x*

Solution for (18-9)/3=9/x* equation:

(18-9)/3=9/x*

We move all terms to the left:

(18-9)/3-(9/x*)=0


Domain of the equation: x*)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+9/x*)+9/3=0

We add all the numbers together, and all the variables

-(+9/x*)+3=0

We get rid of parentheses

-9/x*+3=0

We multiply all the terms by the denominator


3*x*-9=0

Wy multiply elements

3x^2-9=0

a = 3; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·3·(-9)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{3}}{2*3}=\frac{0-6\sqrt{3}}{6}
=-\frac{6\sqrt{3}}{6}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{3}}{2*3}=\frac{0+6\sqrt{3}}{6}
=\frac{6\sqrt{3}}{6}
=\sqrt{3}
$