6/4g-1=g

Solution for 6/4g-1=g equation:

6/4g-1=g

We move all terms to the left:

6/4g-1-(g)=0


Domain of the equation: 4g!=0

g!=0/4

g!=0

g∈R


We add all the numbers together, and all the variables

-1g+6/4g-1=0

We multiply all the terms by the denominator


-1g*4g-1*4g+6=0

Wy multiply elements

-4g^2-4g+6=0

a = -4; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-4)·6
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*-4}=\frac{4-4\sqrt{7}}{-8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*-4}=\frac{4+4\sqrt{7}}{-8}
$