-5-1/2g=4+1/4g

Solution for -5-1/2g=4+1/4g equation:

-5-1/2g=4+1/4g

We move all terms to the left:

-5-1/2g-(4+1/4g)=0


Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R



Domain of the equation: 4g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

-1/2g-(1/4g+4)-5=0

We get rid of parentheses

-1/2g-1/4g-4-5=0

We calculate fractions


(-4g)/8g^2+(-2g)/8g^2-4-5=0

We add all the numbers together, and all the variables

(-4g)/8g^2+(-2g)/8g^2-9=0

We multiply all the terms by the denominator


(-4g)+(-2g)-9*8g^2=0

Wy multiply elements

-72g^2+(-4g)+(-2g)=0

We get rid of parentheses

-72g^2-4g-2g=0

We add all the numbers together, and all the variables

-72g^2-6g=0

a = -72; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-72)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-72}=\frac{0}{-144}
=0
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-72}=\frac{12}{-144}
=-1/12
$