y-y^2=56-15y

Solution for y-y^2=56-15y equation:

y-y^2=56-15y

We move all terms to the left:

y-y^2-(56-15y)=0

We add all the numbers together, and all the variables

-y^2+y-(-15y+56)=0

We add all the numbers together, and all the variables

-1y^2+y-(-15y+56)=0

We get rid of parentheses

-1y^2+y+15y-56=0

We add all the numbers together, and all the variables

-1y^2+16y-56=0

a = -1; b = 16; c = -56;
Δ = b2-4ac
Δ = 162-4·(-1)·(-56)
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{2}}{2*-1}=\frac{-16-4\sqrt{2}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{2}}{2*-1}=\frac{-16+4\sqrt{2}}{-2}
$