y(5-y)=7y

Solution for y(5-y)=7y equation:

y(5-y)=7y

We move all terms to the left:

y(5-y)-(7y)=0

We add all the numbers together, and all the variables

y(-1y+5)-7y=0

We add all the numbers together, and all the variables

-7y+y(-1y+5)=0

We multiply parentheses

-1y^2-7y+5y=0

We add all the numbers together, and all the variables

-1y^2-2y=0

a = -1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-1}=\frac{0}{-2}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-1}=\frac{4}{-2}
=-2
$