7x^2-1=524

Solution for 7x^2-1=524 equation:

7x^2-1=524

We move all terms to the left:

7x^2-1-(524)=0

We add all the numbers together, and all the variables

7x^2-525=0

a = 7; b = 0; c = -525;
Δ = b2-4ac
Δ = 02-4·7·(-525)
Δ = 14700
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:

$\sqrt{\Delta}=\sqrt{14700}=\sqrt{4900*3}=\sqrt{4900}*\sqrt{3}=70\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70\sqrt{3}}{2*7}=\frac{0-70\sqrt{3}}{14}
=-\frac{70\sqrt{3}}{14}
=-5\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70\sqrt{3}}{2*7}=\frac{0+70\sqrt{3}}{14}
=\frac{70\sqrt{3}}{14}
=5\sqrt{3}
$