(y-14)(y+4)=y-14

Solution for (y-14)(y+4)=y-14 equation:

(y-14)(y+4)=y-14

We move all terms to the left:

(y-14)(y+4)-(y-14)=0

We get rid of parentheses

(y-14)(y+4)-y+14=0

We multiply parentheses ..

(+y^2+4y-14y-56)-y+14=0

We add all the numbers together, and all the variables

(+y^2+4y-14y-56)-1y+14=0

We get rid of parentheses

y^2+4y-14y-1y-56+14=0

We add all the numbers together, and all the variables

y^2-11y-42=0

a = 1; b = -11; c = -42;
Δ = b2-4ac
Δ = -112-4·1·(-42)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*1}=\frac{-6}{2}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*1}=\frac{28}{2}
=14
$