3a^2+1=100

Solution for 3a^2+1=100 equation:

3a^2+1=100

We move all terms to the left:

3a^2+1-(100)=0

We add all the numbers together, and all the variables

3a^2-99=0

a = 3; b = 0; c = -99;
Δ = b2-4ac
Δ = 02-4·3·(-99)
Δ = 1188
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:

$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{33}}{2*3}=\frac{0-6\sqrt{33}}{6}
=-\frac{6\sqrt{33}}{6}
=-\sqrt{33}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{33}}{2*3}=\frac{0+6\sqrt{33}}{6}
=\frac{6\sqrt{33}}{6}
=\sqrt{33}
$