10x^2-2=x^2+7

Solution for 10x^2-2=x^2+7 equation:

10x^2-2=x^2+7

We move all terms to the left:

10x^2-2-(x^2+7)=0

We get rid of parentheses

10x^2-x^2-7-2=0

We add all the numbers together, and all the variables

9x^2-9=0

a = 9; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·9·(-9)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*9}=\frac{-18}{18}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*9}=\frac{18}{18}
=1
$