2a^2+8a+10=a^2

Solution for 2a^2+8a+10=a^2 equation:

2a^2+8a+10=a^2

We move all terms to the left:

2a^2+8a+10-(a^2)=0

determiningTheFunctionDomain
2a^2-a^2+8a+10=0

We add all the numbers together, and all the variables

a^2+8a+10=0

a = 1; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·1·10
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{6}}{2*1}=\frac{-8-2\sqrt{6}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{6}}{2*1}=\frac{-8+2\sqrt{6}}{2}
$