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)=0


Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R



Domain of the equation: 2g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -4; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·(-4)·2
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*-4}=\frac{8-4\sqrt{6}}{-8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*-4}=\frac{8+4\sqrt{6}}{-8}
$