7x^2-1=132

Solution for 7x^2-1=132 equation:

7x^2-1=132

We move all terms to the left:

7x^2-1-(132)=0

We add all the numbers together, and all the variables

7x^2-133=0

a = 7; b = 0; c = -133;
Δ = b2-4ac
Δ = 02-4·7·(-133)
Δ = 3724
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:

$\sqrt{\Delta}=\sqrt{3724}=\sqrt{196*19}=\sqrt{196}*\sqrt{19}=14\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{19}}{2*7}=\frac{0-14\sqrt{19}}{14}
=-\frac{14\sqrt{19}}{14}
=-\sqrt{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{19}}{2*7}=\frac{0+14\sqrt{19}}{14}
=\frac{14\sqrt{19}}{14}
=\sqrt{19}
$