1/2g-4=2g-1/2g+4

Solution for 1/2g-4=2g-1/2g+4 equation:

1/2g-4=2g-1/2g+4

We move all terms to the left:

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


Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R



Domain of the equation: 2g+4)!=0

g∈R


We get rid of parentheses

1/2g-2g+1/2g-4-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-2g*2g-4*2g-4*2g+2=0

Wy multiply elements

-4g^2-8g-8g+2=0

We add all the numbers together, and all the variables

-4g^2-16g+2=0

a = -4; b = -16; c = +2;
Δ = b2-4ac
Δ = -162-4·(-4)·2
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12\sqrt{2}}{2*-4}=\frac{16-12\sqrt{2}}{-8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12\sqrt{2}}{2*-4}=\frac{16+12\sqrt{2}}{-8}
$