30=-6y(y+8)

Solution for 30=-6y(y+8) equation:

30=-6y(y+8)

We move all terms to the left:

30-(-6y(y+8))=0


We calculate terms in parentheses: -(-6y(y+8)), so:

-6y(y+8)

We multiply parentheses

-6y^2-48y

Back to the equation:

-(-6y^2-48y)


We get rid of parentheses

6y^2+48y+30=0

a = 6; b = 48; c = +30;
Δ = b2-4ac
Δ = 482-4·6·30
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{11}}{2*6}=\frac{-48-12\sqrt{11}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{11}}{2*6}=\frac{-48+12\sqrt{11}}{12}
$