90/y-y=13

Solution for 90/y-y=13 equation:

90/y-y=13

We move all terms to the left:

90/y-y-(13)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-1y+90/y-13=0

We multiply all the terms by the denominator


-1y*y-13*y+90=0

We add all the numbers together, and all the variables

-13y-1y*y+90=0

Wy multiply elements

-1y^2-13y+90=0

a = -1; b = -13; c = +90;
Δ = b2-4ac
Δ = -132-4·(-1)·90
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*-1}=\frac{-10}{-2}
=+5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*-1}=\frac{36}{-2}
=-18
$