4a+9=a2-1

Solution for 4a+9=a2-1 equation:

4a+9=a2-1

We move all terms to the left:

4a+9-(a2-1)=0

We add all the numbers together, and all the variables

-(+a^2-1)+4a+9=0

We get rid of parentheses

-a^2+4a+1+9=0

We add all the numbers together, and all the variables

-1a^2+4a+10=0

a = -1; b = 4; c = +10;
Δ = b2-4ac
Δ = 42-4·(-1)·10
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{14}}{2*-1}=\frac{-4-2\sqrt{14}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{14}}{2*-1}=\frac{-4+2\sqrt{14}}{-2}
$