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-(r+13)=0

We get rid of parentheses

40/r-r-13=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-13r-r*r+40=0

Wy multiply elements

-1r^2-13r+40=0

a = -1; b = -13; c = +40;
Δ = b2-4ac
Δ = -132-4·(-1)·40
Δ = 329
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{-(-13)-\sqrt{329}}{2*-1}=\frac{13-\sqrt{329}}{-2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{329}}{2*-1}=\frac{13+\sqrt{329}}{-2}
$