9x^2-21=9+x^2

Solution for 9x^2-21=9+x^2 equation:

9x^2-21=9+x^2

We move all terms to the left:

9x^2-21-(9+x^2)=0

We get rid of parentheses

9x^2-x^2-9-21=0

We add all the numbers together, and all the variables

8x^2-30=0

a = 8; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·8·(-30)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*8}=\frac{0-8\sqrt{15}}{16}
=-\frac{8\sqrt{15}}{16}
=-\frac{\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*8}=\frac{0+8\sqrt{15}}{16}
=\frac{8\sqrt{15}}{16}
=\frac{\sqrt{15}}{2}
$