1/2g+1=1/4g+3

Solution for 1/2g+1=1/4g+3 equation:

1/2g+1=1/4g+3

We move all terms to the left:

1/2g+1-(1/4g+3)=0


Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R



Domain of the equation: 4g+3)!=0

g∈R


We get rid of parentheses

1/2g-1/4g-3+1=0

We calculate fractions


4g/8g^2+(-2g)/8g^2-3+1=0

We add all the numbers together, and all the variables

4g/8g^2+(-2g)/8g^2-2=0

We multiply all the terms by the denominator


4g+(-2g)-2*8g^2=0

Wy multiply elements

-16g^2+4g+(-2g)=0

We get rid of parentheses

-16g^2+4g-2g=0

We add all the numbers together, and all the variables

-16g^2+2g=0

a = -16; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-16)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-16}=\frac{-4}{-32}
=1/8
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-16}=\frac{0}{-32}
=0
$