(y-14)(y+6)=y-14

Solution for (y-14)(y+6)=y-14 equation:

(y-14)(y+6)=y-14

We move all terms to the left:

(y-14)(y+6)-(y-14)=0

We get rid of parentheses

(y-14)(y+6)-y+14=0

We multiply parentheses ..

(+y^2+6y-14y-84)-y+14=0

We add all the numbers together, and all the variables

(+y^2+6y-14y-84)-1y+14=0

We get rid of parentheses

y^2+6y-14y-1y-84+14=0

We add all the numbers together, and all the variables

y^2-9y-70=0

a = 1; b = -9; c = -70;
Δ = b2-4ac
Δ = -92-4·1·(-70)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-19}{2*1}=\frac{-10}{2}
=-5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+19}{2*1}=\frac{28}{2}
=14
$