999-1=a*a-9

Solution for 999-1=a*a-9 equation:

999-1=a*a-9

We move all terms to the left:

999-1-(a*a-9)=0

We add all the numbers together, and all the variables

-(a*a-9)+998=0

We get rid of parentheses

-a*a+9+998=0

We add all the numbers together, and all the variables

-a*a+1007=0

Wy multiply elements

-1a^2+1007=0

a = -1; b = 0; c = +1007;
Δ = b2-4ac
Δ = 02-4·(-1)·1007
Δ = 4028
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4028}=\sqrt{4*1007}=\sqrt{4}*\sqrt{1007}=2\sqrt{1007}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1007}}{2*-1}=\frac{0-2\sqrt{1007}}{-2}
=-\frac{2\sqrt{1007}}{-2}
=-\frac{\sqrt{1007}}{-1}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1007}}{2*-1}=\frac{0+2\sqrt{1007}}{-2}
=\frac{2\sqrt{1007}}{-2}
=\frac{\sqrt{1007}}{-1}
$