6y^2-24-54=0

Solution for 6y^2-24-54=0 equation:

6y^2-24-54=0

We add all the numbers together, and all the variables

6y^2-78=0

a = 6; b = 0; c = -78;
Δ = b2-4ac
Δ = 02-4·6·(-78)
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{13}}{2*6}=\frac{0-12\sqrt{13}}{12}
=-\frac{12\sqrt{13}}{12}
=-\sqrt{13}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{13}}{2*6}=\frac{0+12\sqrt{13}}{12}
=\frac{12\sqrt{13}}{12}
=\sqrt{13}
$