r+4.6/r-2.3=3.3

Solution for r+4.6/r-2.3=3.3 equation:

r+4.6/r-2.3=3.3

We move all terms to the left:

r+4.6/r-2.3-(3.3)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

r+4.6/r-5.6=0

We multiply all the terms by the denominator


r*r-(5.6)*r+4.6=0

We multiply parentheses

r*r-5.6r+4.6=0

Wy multiply elements

r^2-5.6r+4.6=0

a = 1; b = -5.6; c = +4.6;
Δ = b2-4ac
Δ = -5.62-4·1·4.6
Δ = 12.96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5.6)-\sqrt{12.96}}{2*1}=\frac{5.6-\sqrt{12.96}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.6)+\sqrt{12.96}}{2*1}=\frac{5.6+\sqrt{12.96}}{2}
$