(2-y)(5-y)=y

Solution for (2-y)(5-y)=y equation:

(2-y)(5-y)=y

We move all terms to the left:

(2-y)(5-y)-(y)=0

We add all the numbers together, and all the variables

(-1y+2)(-1y+5)-y=0

We add all the numbers together, and all the variables

-1y+(-1y+2)(-1y+5)=0

We multiply parentheses ..

(+y^2-5y-2y+10)-1y=0

We get rid of parentheses

y^2-5y-2y-1y+10=0

We add all the numbers together, and all the variables

y^2-8y+10=0

a = 1; b = -8; c = +10;
Δ = b2-4ac
Δ = -82-4·1·10
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{6}}{2*1}=\frac{8-2\sqrt{6}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{6}}{2*1}=\frac{8+2\sqrt{6}}{2}
$