1/8g+8=g

Solution for 1/8g+8=g equation:

1/8g+8=g

We move all terms to the left:

1/8g+8-(g)=0


Domain of the equation: 8g!=0

g!=0/8

g!=0

g∈R


We add all the numbers together, and all the variables

-1g+1/8g+8=0

We multiply all the terms by the denominator


-1g*8g+8*8g+1=0

Wy multiply elements

-8g^2+64g+1=0

a = -8; b = 64; c = +1;
Δ = b2-4ac
Δ = 642-4·(-8)·1
Δ = 4128
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:

$\sqrt{\Delta}=\sqrt{4128}=\sqrt{16*258}=\sqrt{16}*\sqrt{258}=4\sqrt{258}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{258}}{2*-8}=\frac{-64-4\sqrt{258}}{-16}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{258}}{2*-8}=\frac{-64+4\sqrt{258}}{-16}
$