r=3/7r-2

Solution for r=3/7r-2 equation:

r=3/7r-2

We move all terms to the left:

r-(3/7r-2)=0


Domain of the equation: 7r-2)!=0

r∈R


We get rid of parentheses

r-3/7r+2=0

We multiply all the terms by the denominator


r*7r+2*7r-3=0

Wy multiply elements

7r^2+14r-3=0

a = 7; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·7·(-3)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{70}}{2*7}=\frac{-14-2\sqrt{70}}{14}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{70}}{2*7}=\frac{-14+2\sqrt{70}}{14}
$