40/y=13-y

Solution for 40/y=13-y equation:

40/y=13-y

We move all terms to the left:

40/y-(13-y)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

40/y+1y-13=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

y^2-13y+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:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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