3a^2+5=a^2+9.5

Solution for 3a^2+5=a^2+9.5 equation:

3a^2+5=a^2+9.5

We move all terms to the left:

3a^2+5-(a^2+9.5)=0

We get rid of parentheses

3a^2-a^2-9.5+5=0

We add all the numbers together, and all the variables

2a^2-4.5=0

a = 2; b = 0; c = -4.5;
Δ = b2-4ac
Δ = 02-4·2·(-4.5)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*2}=\frac{-6}{4}
=-1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*2}=\frac{6}{4}
=1+1/2
$