180=2y(y+7)

Solution for 180=2y(y+7) equation:

180=2y(y+7)

We move all terms to the left:

180-(2y(y+7))=0


We calculate terms in parentheses: -(2y(y+7)), so:

2y(y+7)

We multiply parentheses

2y^2+14y

Back to the equation:

-(2y^2+14y)


We get rid of parentheses

-2y^2-14y+180=0

a = -2; b = -14; c = +180;
Δ = b2-4ac
Δ = -142-4·(-2)·180
Δ = 1636
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:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{409}}{2*-2}=\frac{14-2\sqrt{409}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{409}}{2*-2}=\frac{14+2\sqrt{409}}{-4}
$