10=y(7-y)

Solution for 10=y(7-y) equation:

10=y(7-y)

We move all terms to the left:

10-(y(7-y))=0

We add all the numbers together, and all the variables

-(y(-1y+7))+10=0


We calculate terms in parentheses: -(y(-1y+7)), so:

y(-1y+7)

We multiply parentheses

-1y^2+7y

Back to the equation:

-(-1y^2+7y)


We get rid of parentheses

1y^2-7y+10=0

We add all the numbers together, and all the variables

y^2-7y+10=0

a = 1; b = -7; c = +10;
Δ = b2-4ac
Δ = -72-4·1·10
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*1}=\frac{4}{2}
=2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*1}=\frac{10}{2}
=5
$