38r=3/7r

Solution for 38r=3/7r equation:

38r=3/7r

We move all terms to the left:

38r-(3/7r)=0


Domain of the equation: 7r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

38r-(+3/7r)=0

We get rid of parentheses

38r-3/7r=0

We multiply all the terms by the denominator


38r*7r-3=0

Wy multiply elements

266r^2-3=0

a = 266; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·266·(-3)
Δ = 3192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3192}=\sqrt{4*798}=\sqrt{4}*\sqrt{798}=2\sqrt{798}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{798}}{2*266}=\frac{0-2\sqrt{798}}{532}
=-\frac{2\sqrt{798}}{532}
=-\frac{\sqrt{798}}{266}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{798}}{2*266}=\frac{0+2\sqrt{798}}{532}
=\frac{2\sqrt{798}}{532}
=\frac{\sqrt{798}}{266}
$