40/r=13-r

Solution for 40/r=13-r equation:

40/r=13-r

We move all terms to the left:

40/r-(13-r)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

40/r-(-1r+13)=0

We get rid of parentheses

40/r+1r-13=0

We multiply all the terms by the denominator


1r*r-13*r+40=0

We add all the numbers together, and all the variables

-13r+1r*r+40=0

Wy multiply elements

r^2-13r+40=0

a = 1; b = -13; c = +40;
Δ = b2-4ac
Δ = -132-4·1·40
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3}{2*1}=\frac{10}{2}
=5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3}{2*1}=\frac{16}{2}
=8
$