(y+7)(y-2)=y

Solution for (y+7)(y-2)=y equation:

(y+7)(y-2)=y

We move all terms to the left:

(y+7)(y-2)-(y)=0

We add all the numbers together, and all the variables

-1y+(y+7)(y-2)=0

We multiply parentheses ..

(+y^2-2y+7y-14)-1y=0

We get rid of parentheses

y^2-2y+7y-1y-14=0

We add all the numbers together, and all the variables

y^2+4y-14=0

a = 1; b = 4; c = -14;
Δ = b2-4ac
Δ = 42-4·1·(-14)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{2}}{2*1}=\frac{-4-6\sqrt{2}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{2}}{2*1}=\frac{-4+6\sqrt{2}}{2}
$