g(2)=2(2)^2+1

Solution for g(2)=2(2)^2+1 equation:

g(2)=2(2)^2+1

We move all terms to the left:

g(2)-(2(2)^2+1)=0

We add all the numbers together, and all the variables

g^2-485=0

a = 1; b = 0; c = -485;
Δ = b2-4ac
Δ = 02-4·1·(-485)
Δ = 1940
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1940}=\sqrt{4*485}=\sqrt{4}*\sqrt{485}=2\sqrt{485}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{485}}{2*1}=\frac{0-2\sqrt{485}}{2}
=-\frac{2\sqrt{485}}{2}
=-\sqrt{485}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{485}}{2*1}=\frac{0+2\sqrt{485}}{2}
=\frac{2\sqrt{485}}{2}
=\sqrt{485}
$