3/7g=g

Solution for 3/7g=g equation:

3/7g=g

We move all terms to the left:

3/7g-(g)=0


Domain of the equation: 7g!=0

g!=0/7

g!=0

g∈R


We add all the numbers together, and all the variables

-1g+3/7g=0

We multiply all the terms by the denominator


-1g*7g+3=0

Wy multiply elements

-7g^2+3=0

a = -7; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-7)·3
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*-7}=\frac{0-2\sqrt{21}}{-14}
=-\frac{2\sqrt{21}}{-14}
=-\frac{\sqrt{21}}{-7}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*-7}=\frac{0+2\sqrt{21}}{-14}
=\frac{2\sqrt{21}}{-14}
=\frac{\sqrt{21}}{-7}
$