1/8g+7=g

Solution for 1/8g+7=g equation:

1/8g+7=g

We move all terms to the left:

1/8g+7-(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+7=0

We multiply all the terms by the denominator


-1g*8g+7*8g+1=0

Wy multiply elements

-8g^2+56g+1=0

a = -8; b = 56; c = +1;
Δ = b2-4ac
Δ = 562-4·(-8)·1
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-12\sqrt{22}}{2*-8}=\frac{-56-12\sqrt{22}}{-16}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+12\sqrt{22}}{2*-8}=\frac{-56+12\sqrt{22}}{-16}
$