First, we put the constant in the right-hand side :
2a^2+8a-5=0
<=>2a^2+8a=5
Then we want to transform 2a^2+8a to something like (a+b)^2
Recall : (color(blue)x+color(red)y)^2 = color(blue)(x^2) + color(green)2*color(blue)xcolor(red)y + color(red)(y^2)
Here we have 2a^2 + 8a
<=> 2xx(color(blue)(a^2)+4a)
<=> 2xx(color(blue)(a^2)+color(green)2*color(blue)a*color(red)2) (Then "y" = 2)
<=> 2xx(color(blue)(a^2)+color(green)2*color(blue)a*color(red)2+color(red)(2^2)-2^2) (We added and subtract "y^2" for factorize later)
<=> 2xx((a+2)^2-4)
Put the last expression inside the equality :
2a^2+8a=5
<=> 2xx((a+2)^2-4)=5
<=> 2xx(a+2)^2 - 8 = 5
<=> 2xx(a+2)^2 = 13
<=>(a+2)^2 = 13/2
<=>a+2 = sqrt(13/2) or a+2 = -sqrt(13/2)
Then a =+-sqrt(13/2)-2
