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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(4(y-5)), so:

4(y-5)

We multiply parentheses

4y-20

Back to the equation:

-(4y-20)


We get rid of parentheses

y^2-5y-5y-4y+25+20=0

We add all the numbers together, and all the variables

y^2-14y+45=0

a = 1; b = -14; c = +45;
Δ = b2-4ac
Δ = -142-4·1·45
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{-(-14)-4}{2*1}=\frac{10}{2}
=5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4}{2*1}=\frac{18}{2}
=9
$