(5-y)(y-5)=-4

Solution for (5-y)(y-5)=-4 equation:

(5-y)(y-5)=-4

We move all terms to the left:

(5-y)(y-5)-(-4)=0

We add all the numbers together, and all the variables

(-1y+5)(y-5)-(-4)=0

We add all the numbers together, and all the variables

(-1y+5)(y-5)+4=0

We multiply parentheses ..

(-1y^2+5y+5y-25)+4=0

We get rid of parentheses

-1y^2+5y+5y-25+4=0

We add all the numbers together, and all the variables

-1y^2+10y-21=0

a = -1; b = 10; c = -21;
Δ = b2-4ac
Δ = 102-4·(-1)·(-21)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*-1}=\frac{-14}{-2}
=+7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*-1}=\frac{-6}{-2}
=+3
$