6y^2+27-459=0

Solution for 6y^2+27-459=0 equation:

6y^2+27-459=0

We add all the numbers together, and all the variables

6y^2-432=0

a = 6; b = 0; c = -432;
Δ = b2-4ac
Δ = 02-4·6·(-432)
Δ = 10368
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:

$\sqrt{\Delta}=\sqrt{10368}=\sqrt{5184*2}=\sqrt{5184}*\sqrt{2}=72\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{2}}{2*6}=\frac{0-72\sqrt{2}}{12}
=-\frac{72\sqrt{2}}{12}
=-6\sqrt{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{2}}{2*6}=\frac{0+72\sqrt{2}}{12}
=\frac{72\sqrt{2}}{12}
=6\sqrt{2}
$