g(2)=4(2)^2-3(2)+5

Solution for g(2)=4(2)^2-3(2)+5 equation:

g(2)=4(2)^2-3(2)+5

We move all terms to the left:

g(2)-(4(2)^2-3(2)+5)=0

We add all the numbers together, and all the variables

g^2-1737=0

a = 1; b = 0; c = -1737;
Δ = b2-4ac
Δ = 02-4·1·(-1737)
Δ = 6948
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:

$\sqrt{\Delta}=\sqrt{6948}=\sqrt{36*193}=\sqrt{36}*\sqrt{193}=6\sqrt{193}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{193}}{2*1}=\frac{0-6\sqrt{193}}{2}
=-\frac{6\sqrt{193}}{2}
=-3\sqrt{193}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{193}}{2*1}=\frac{0+6\sqrt{193}}{2}
=\frac{6\sqrt{193}}{2}
=3\sqrt{193}
$