r+4.6/r-2.3=3

Solution for r+4.6/r-2.3=3 equation:

r+4.6/r-2.3=3

We move all terms to the left:

r+4.6/r-2.3-(3)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

r+4.6/r-5.3=0

We multiply all the terms by the denominator


r*r-(5.3)*r+4.6=0

We multiply parentheses

r*r-5.3r+4.6=0

Wy multiply elements

r^2-5.3r+4.6=0

a = 1; b = -5.3; c = +4.6;
Δ = b2-4ac
Δ = -5.32-4·1·4.6
Δ = 9.69
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{-(-5.3)-\sqrt{9.69}}{2*1}=\frac{5.3-\sqrt{9.69}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.3)+\sqrt{9.69}}{2*1}=\frac{5.3+\sqrt{9.69}}{2}
$