5/8g-6=1/4g,g

Solution for 5/8g-6=1/4g,g equation:

5/8g-6=1/4g.g

We move all terms to the left:

5/8g-6-(1/4g.g)=0


Domain of the equation: 8g!=0

g!=0/8

g!=0

g∈R



Domain of the equation: 4g.g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

5/8g-(+1/4g.g)-6=0

We get rid of parentheses

5/8g-1/4g.g-6=0

We calculate fractions


20g/32g^2+(-8g)/32g^2-6=0

We multiply all the terms by the denominator


20g+(-8g)-6*32g^2=0

Wy multiply elements

-192g^2+20g+(-8g)=0

We get rid of parentheses

-192g^2+20g-8g=0

We add all the numbers together, and all the variables

-192g^2+12g=0

a = -192; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-192)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-192}=\frac{-24}{-384}
=1/16
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-192}=\frac{0}{-384}
=0
$