6y^2+72y=-192

Solution for 6y^2+72y=-192 equation:

6y^2+72y=-192

We move all terms to the left:

6y^2+72y-(-192)=0

We add all the numbers together, and all the variables

6y^2+72y+192=0

a = 6; b = 72; c = +192;
Δ = b2-4ac
Δ = 722-4·6·192
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-24}{2*6}=\frac{-96}{12}
=-8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+24}{2*6}=\frac{-48}{12}
=-4
$