7x^2+24x-2=x^2-2

Solution for 7x^2+24x-2=x^2-2 equation:

7x^2+24x-2=x^2-2

We move all terms to the left:

7x^2+24x-2-(x^2-2)=0

We get rid of parentheses

7x^2-x^2+24x+2-2=0

We add all the numbers together, and all the variables

6x^2+24x=0

a = 6; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·6·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*6}=\frac{-48}{12}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*6}=\frac{0}{12}
=0
$