6x^2-1=55

Solution for 6x^2-1=55 equation:

6x^2-1=55

We move all terms to the left:

6x^2-1-(55)=0

We add all the numbers together, and all the variables

6x^2-56=0

a = 6; b = 0; c = -56;
Δ = b2-4ac
Δ = 02-4·6·(-56)
Δ = 1344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{21}}{2*6}=\frac{0-8\sqrt{21}}{12}
=-\frac{8\sqrt{21}}{12}
=-\frac{2\sqrt{21}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{21}}{2*6}=\frac{0+8\sqrt{21}}{12}
=\frac{8\sqrt{21}}{12}
=\frac{2\sqrt{21}}{3}
$