g(1/2)=3*1/2(2)

Solution for g(1/2)=3*1/2(2) equation:

g(1/2)=3*1/2(2)

We move all terms to the left:

g(1/2)-(3*1/2(2))=0

We add all the numbers together, and all the variables

g(+1/2)-(+3*1/22)=0

We multiply parentheses

g^2-(+3*1/22)=0

We get rid of parentheses

g^2-3*1/22=0

We multiply all the terms by the denominator


g^2*22-3*1=0

We add all the numbers together, and all the variables

g^2*22-3=0

Wy multiply elements

22g^2-3=0

a = 22; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·22·(-3)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*22}=\frac{0-2\sqrt{66}}{44}
=-\frac{2\sqrt{66}}{44}
=-\frac{\sqrt{66}}{22}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*22}=\frac{0+2\sqrt{66}}{44}
=\frac{2\sqrt{66}}{44}
=\frac{\sqrt{66}}{22}
$