6r*1/2r=9r=

Solution for 6r*1/2r=9r= equation:

6r*1/2r=9r=

We move all terms to the left:

6r*1/2r-(9r)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We add all the numbers together, and all the variables

-9r+6r*1/2r=0

We multiply all the terms by the denominator


-9r*2r+6r*1=0

Wy multiply elements

-18r^2+6r=0

a = -18; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-18)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-18}=\frac{-12}{-36}
=1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-18}=\frac{0}{-36}
=0
$