144=3y(y+18)

Solution for 144=3y(y+18) equation:

144=3y(y+18)

We move all terms to the left:

144-(3y(y+18))=0


We calculate terms in parentheses: -(3y(y+18)), so:

3y(y+18)

We multiply parentheses

3y^2+54y

Back to the equation:

-(3y^2+54y)


We get rid of parentheses

-3y^2-54y+144=0

a = -3; b = -54; c = +144;
Δ = b2-4ac
Δ = -542-4·(-3)·144
Δ = 4644
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:

$\sqrt{\Delta}=\sqrt{4644}=\sqrt{36*129}=\sqrt{36}*\sqrt{129}=6\sqrt{129}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{129}}{2*-3}=\frac{54-6\sqrt{129}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{129}}{2*-3}=\frac{54+6\sqrt{129}}{-6}
$