(13-y)y=10

Solution for (13-y)y=10 equation:

(13-y)y=10

We move all terms to the left:

(13-y)y-(10)=0

We add all the numbers together, and all the variables

(-1y+13)y-10=0

We multiply parentheses

-1y^2+13y-10=0

a = -1; b = 13; c = -10;
Δ = b2-4ac
Δ = 132-4·(-1)·(-10)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{129}}{2*-1}=\frac{-13-\sqrt{129}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{129}}{2*-1}=\frac{-13+\sqrt{129}}{-2}
$