7(x^2-2)-1=48

Solution for 7(x^2-2)-1=48 equation:

7(x^2-2)-1=48

We move all terms to the left:

7(x^2-2)-1-(48)=0

We add all the numbers together, and all the variables

7(x^2-2)-49=0

We multiply parentheses

7x^2-14-49=0

We add all the numbers together, and all the variables

7x^2-63=0

a = 7; b = 0; c = -63;
Δ = b2-4ac
Δ = 02-4·7·(-63)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42}{2*7}=\frac{-42}{14}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42}{2*7}=\frac{42}{14}
=3
$