6y^2-1=53

Solution for 6y^2-1=53 equation:

6y^2-1=53

We move all terms to the left:

6y^2-1-(53)=0

We add all the numbers together, and all the variables

6y^2-54=0

a = 6; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·6·(-54)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*6}=\frac{-36}{12}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*6}=\frac{36}{12}
=3
$