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

a = 6; b = 72; c = -192;
Δ = b2-4ac
Δ = 722-4·6·(-192)
Δ = 9792
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:

$\sqrt{\Delta}=\sqrt{9792}=\sqrt{576*17}=\sqrt{576}*\sqrt{17}=24\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-24\sqrt{17}}{2*6}=\frac{-72-24\sqrt{17}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+24\sqrt{17}}{2*6}=\frac{-72+24\sqrt{17}}{12}
$