-6y-18=-3y(y+9)

Solution for -6y-18=-3y(y+9) equation:

-6y-18=-3y(y+9)

We move all terms to the left:

-6y-18-(-3y(y+9))=0


We calculate terms in parentheses: -(-3y(y+9)), so:

-3y(y+9)

We multiply parentheses

-3y^2-27y

Back to the equation:

-(-3y^2-27y)


We get rid of parentheses

3y^2+27y-6y-18=0

We add all the numbers together, and all the variables

3y^2+21y-18=0

a = 3; b = 21; c = -18;
Δ = b2-4ac
Δ = 212-4·3·(-18)
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{73}}{2*3}=\frac{-21-3\sqrt{73}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{73}}{2*3}=\frac{-21+3\sqrt{73}}{6}
$