g(4/3)=3^4/3

Solution for g(4/3)=3^4/3 equation:

g(4/3)=3^4/3

We move all terms to the left:

g(4/3)-(3^4/3)=0

We add all the numbers together, and all the variables

g(+4/3)-(3^4/3)=0

We multiply parentheses

4g^2-(3^4/3)=0

We get rid of parentheses

4g^2-3^4/3=0

We multiply all the terms by the denominator


4g^2*3-3^4=0

We add all the numbers together, and all the variables

4g^2*3-81=0

Wy multiply elements

12g^2-81=0

a = 12; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·12·(-81)
Δ = 3888
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:

$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{3}}{2*12}=\frac{0-36\sqrt{3}}{24}
=-\frac{36\sqrt{3}}{24}
=-\frac{3\sqrt{3}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{3}}{2*12}=\frac{0+36\sqrt{3}}{24}
=\frac{36\sqrt{3}}{24}
=\frac{3\sqrt{3}}{2}
$