4g-12(2)=1/2g

Solution for 4g-12(2)=1/2g equation:

4g-12(2)=1/2g

We move all terms to the left:

4g-12(2)-(1/2g)=0


Domain of the equation: 2g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

4g-(+1/2g)-122=0

We get rid of parentheses

4g-1/2g-122=0

We multiply all the terms by the denominator


4g*2g-122*2g-1=0

Wy multiply elements

8g^2-244g-1=0

a = 8; b = -244; c = -1;
Δ = b2-4ac
Δ = -2442-4·8·(-1)
Δ = 59568
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:

$\sqrt{\Delta}=\sqrt{59568}=\sqrt{16*3723}=\sqrt{16}*\sqrt{3723}=4\sqrt{3723}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-244)-4\sqrt{3723}}{2*8}=\frac{244-4\sqrt{3723}}{16}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-244)+4\sqrt{3723}}{2*8}=\frac{244+4\sqrt{3723}}{16}
$